As others have noted, all but one datapoint is consistent with Galleon/Carrack having 30hp, Barquentine/Dhow having 20hp, The one exception being a single case of Carrack taking 5% dmg from Reef. Also as abstractapplic has noted, Barquentines tend to be effected by things similarly to Galleons and Dhow similarly to Carracks. abstractapplic claims that they are the same other than hp, but it would take a massive confounder to account for e.g. the different encounter probabilities (as found by measure, also remarked on below).

Note, per-hex encounter probabilities below don't account for selection effects except that I tended to round up if close call to round up or down. I do count only out-of-port ships that didn't get destroyed in the denominator. Damage numbers don't account for selection effects either.

Reef, Kraken, Iceberg Mefolk and Wyrd Majick Fyre have location dependence as noted by others.

Reef always does at least 1 damage, exponentialish decline with long tail, 3.5-4 average

As noted by abstractapplic, Reefs occur on hexes adjacent to land but not adjacent to ports. I haven't seen anyone mention that for the purpose of this rule, L16 is a land hex. I guess it's a seamount.

The probability of receiving a reef encounter if going through a reef hex is about ~20% for non-Dhow's, and ~4% for Dhows.  Combined with the potentially high damage this makes these a high priority to avoid if not using a Dhow.

Kraken: spiky damage histogram. Spikes decline for higher values (but selection effects?), worse for Carrack/Dhow, and  Carrack/Dhow also seem to lack a low damage component present in the Barquentine/Galleon distribution  . ~3.5 average for Galleon/Barquentine,  ~6.5 for Dhow, ~8 for Carrack.

As others have noted Kraken have "territories". These "territories" actually are just a simple rule as with Reefs:

Kraken territories =  spaces at least a 2 hex gap away from land (where land has the same definition as for Reefs, i.e. L16 is a land hex).

Around 25-30% encounter probability per relevant hex. Combined with the high damage, high priority to avoid for all ships but especially Carrack/Dhow.

You can always avoid Kraken+Reefs by keeping a 1 hex gap between you and land (or L16) when not adjacent to a port. There are minimum length paths that follow this rule between most port combinations except between South Point and either Norwatch and Eastmarch, where a detour is required (a quite significant one for Eastmarch/South Point). 

As noted by others, the target points are in Kraken territory (IMO this is likely a coincidence since that just means they are far at sea). We can avoid going into any additional Kraken territory, but this will require an additional detour (relative to just avoiding reefs) for the western target particularly if avoiding E7 for which we have no data.

Icebergs: dmg roughly consistent with 1d6 as reported by abstractapplic, so about 3.5 average damage. However, Galleons and Carracks seem to take 1 damage more often and Barquentines and Dhows take 1 damage less often. Maybe coincidence?

Icebergs are found from rows 0-2 in summer (Jun-Aug), in rows 0-6 in spring and fall(Sept-May), and in rows 0-10 in winter (Dec-Feb). (Others have remarked on Iceberg seasonality/northernness more generally).

Icebergs are not particularly high probability (<10%) per hex, but would add up if far enough north. Since this voyage will occur in summer, we don't have to worry about icebergs unless taking a significant detour to the north.

Merfolk: Do 0 dmg a lot of time, though unlike abstracapplic I am not convinced it is exactly half. Exponentialish? decline if they do do damage, which can go to high values. About ~2.6 average damage for Galleons, ~1.7 for Barquentines, ~6 for Carracks, ~4 for Dhows.

As noted by abstractapplic Merfolk have two zones.

Most Merfolk reports form a giant triangularish donut centered around the northeast corner of J8. The donut looks like it should include F7 and L11, but there are no reports from there, and looks like it should not include O5, but O5 does have one Merfolk report. In the case of F7 this is probably just chance, since it's not visited a lot. All other reports are in another Merfolk zone southwest of Westengard. The giant donut occupies most of the center of the map and is hard to avoid, so should be analyzed further. 

Merfolk have a ~9% probability per hex for Galleons, ~2.7% for Barquentines, and ~1.8% for Carrack/Dhow. 

I have also noticed that relative to the low popularity of these hexes, Merfolk are significantly more likely to be encountered in the southwest region. I have not checked if this is connected with the ship type stats, but I will leave this for now since we don't need to go to that region. 

Wyrd Majick Fyre: high damage, mostly 7 or less, but with tail (exponentialish?) 4-5 average for all except Dhow, which gets ~1.2.

As others have reported, Wyrd Majick Fyre mostly occurs around J8 (almost but not quite aligned with the Merfolk donut hole), with a few random-looking other instances. It is a >10% encounter in these hexes making them important to avoid for non-Dhows even if they did not also have Reefs (which they do).

Pirates: as abstractapplic noted does not do 1 dmg (but does do zero, very often, or 2d3? but with a long tail. ~3.1 average for Galleons/barquentine, ~4.4 for Dhow and ~5.29 for Carrack.

As measure noted, Galleons receive more pirate attacks. Per-hex encounter probability of ~12% for Galleons and ~4% for everything else. Todo: check to see if this depends e.g. on mission type.

Storm: usually 0-7dmg. some tail. 2.5-2.6 average damage. Around ~7% chance per hex regardless of ship type.

Sharks: as abbstractapplic noted, dmg is consistent with min(2d4)-1. As with Pirates,  Per-hex encounter probability of ~12% for Galleons and ~4% for everything else. While not as damaging as Pirates, adds a reason to avoid Galleons.

Harpies:  Galleons and Barquentines seem to take 0 dmg 2/3 of the time, and 1-2 damage 1/3 of the time. Carracks and Dhows seem to take 0 dmg 1/3 of the time, and 1-4 dmg 2/3 of the time. So, theoretically 0.5 average for Galleons/Barquentines and 1.7 average for Carracks/Dhows

Per-hex encounter probability is ~9% for Galleons and ~4% for others, but per-hex damage from Harpies is still less for Galleons than for Carracks and Barquentines.

Dragon: long tail in damage; peaks later for Carracks/Dhows; ~3.4 average for Barquentine, ~3.7 Galleon, ~5 for Dhow, ~7.5 for Carracks. 

Per-hex encounter probability is ~2% for Galleons, ~0.06% for barquentines, ~0.3% for Carracks and Dhows. In terms of average damage per hex the extra encounter probability for Galleons more than makes up for them taking less damage per event than Carracks and Dhows.

Looking at the encounter types that are initally seem location-independent, we have an average per hex movement cost in damage points, by ship type, of:

Ship/encounter| Pirates | Storm | Sharks | Harpies | Dragon | Total

Galleon              | 0.36     | 0.17    | 0.11     | 0.039    | 0.073    |  0.75

Carrack              | 0.19     | 0.18    | 0.34     | 0.069    | 0.021    | 0.50

Barquentine     | 0.11     | 0.18    | 0.034   | 0.021    | 0.019    | 0.37

Dhow                | 0.16     | 0.16    | 0.036   | 0.058    | 0.017    | 0.44

Taking into account ship hp, the Carrack looks the best here, with ~60 hexes of movement.

We are also likely going to go into Merfolk territory though, which adds an additional cost:

Galleon: 0.24

Carrack: 0.11

Barquentine: 0.044

Dhow: 0.072

It's looking a lot more even here between Carrack/Barquentine, but still slightly favouring Carrack. Since not all of the trip will be in Merfolk territory, might as well go for the Carrack?

One other thing - this cost assumes uniformity of Merfolk, though I actually think the southwest merfolk are more aggressive. Should adjust to account for that later.

We also want to minimize chance of sinking, not damage to be repaired in port. If confident average damage will be tolerable, we might want to reduce long tails rather than average damage. This could favour the Barquentine.

Dhow has less chance of hitting Reefs. Going to the east target, we can take a shortcut through Reefs and might want to consider a Dhow for that.

Additional dmg per Reef hex (v. non-Reef):

Galleon: 0.79

Carrack:  0.76

Barquentine: 0.68

Dhow: 0.17

Going to the West target, we might want to take a shortcut through Kraken territory, for which a Barquentine might be more suitable than a Carrack.

Additional damage per Kraken hex (v. non-Kraken):

Galleon: 0.99

Carrack: 2.04

Barquentine: 0.95

Dhow 1.59

We also might want to avoid E7, for which we have no data. There be dragons. I mean ... in-universe hypothetical squared dragons.

Also, early on I noted down some hexes where >1/5 of ships passing through were destroyed. They include some hexes which should not be especially dangerous from the above info, but this could just be that the routes also pass through dangerous hexes. Anyway, something to look at with further analysis, and maybe avoid if not costly to do so.

With all the above in mind, candidate routes and other info messily drawn on the map:

EditL map deleted and moved to imgur since it wasn't being spoiler properly

imgur link

When counting hexes, I don't count the port since these seem safe from the data.

For the west target:

Route A is the obvious choice taking all the above at face value. With a return trip, it will involve 27 hexes, of which 22 are Merfolk hexes and 1 Kraken.

Route B avoids the unknowns of E7. It's the same overall length including Merfolk length as Route A, but has 5 Kraken hexes on the round trip.

Route C also expensively avoids E7. It's 37 hexes, of which 20  are Merfolk hexes and 1 Kraken. No way that's going to be worth it.

I also added route G later which minimizes distance (and avoids E7) at the cost of additional Kraken hexes. 25 hexes, of which 20 Merfolk and  9 Kraken.

All of these routes involve >1/5 destroyed hexes, but I'm not prioritizing avoiding these super hard atm on the theory that these hexes will turn out to just be on paths that go through other dangerous stuff or are long.

For the east target:

Route D avoids reefs,  but is long and goes through Merfolk territory. It also goes through some >1/5 destroyed hexes. 21 hexes round trip, of which 18 Merfolk and 1 Kraken.

Route E takes 2 reefs to shortcut. 19 hexes round trip, or which 4 reefs and 1 Kraken.

Route F takes 3 reefs to shorten the path a bit more. 17 hexes round trip, of which 6 reefs and 1 Kraken. This is the shortest possible path given the constraint that you can't go across land.

So, expected damage for each route :

route/ship type   | Galleon | Carrack | Barquentine | Dhow

Route A (west)    |  26.5      | 17.9       | 11.8               | 15.0

Route B (west)    | 30.5       | 26.0       | 15.6               | 21.3

Route C (west)    | 33.5       | 22.6       | 15.4               | 19.2

Route G (west)   | 32.4       | 33.0       | 18.6               | 26.6

Route D (east)    | 21.1       | 14.4       | 9.5                 | 12.0

Route E (east)    | 18.4       | 14.6       | 10.7               | 10.6

Route F (east)    | 18.4       | 15.1       | 11.3               | 10.0

Route A looks so much better than the other western choices that I am willing to have the sailors brave the squared dragons. Barquentine looking like the best choice even with only 20 hp.

For the eastern target, Route D looks good with either a Barquentine or a Carrack, or Route F with a Dhow. Some considerations: Route D does go through >1/5 destroyed hexes, so I should try to find out if that really is a problem. On the other hand, the Dhow has low chance to hit a Reef but not low damage if it does get hit - high variance is risky. On balance, I pick the Barquentine on D for now.

So, for now I pick: 

"The Bloody Diamond, a Barquentine captained by Angus MacDougal" on Route A (Q6-P6-O6-N6-M5-L5-K5-J5-I5-H5-G5-F5-F6-E7-E8) and back by the same route.

"The Saucy Heart, a Barquentine captained by Erin Aubrey" on Route D (Q6-P6-O6-N6-M7-M8-L8-K9-K10-K11-L12-L13) and back by the same route.

My selected routes A and D are the same ones chosen by abstractapplic, but I use two Barquentines whereas abstractapplic uses a Galleon and a Barquentine.

Yonge selected Route F to go to the east target and for the west first selected something that looks like it should be equivalent to my Route B, in terms of length and types of hexes it goes in, but at the bottom of the comment changes it (why?) to add some additional dilly-dallying in Kraken territory. Yonge chose a Galleon and a Carrack.

measure picked two Dhows (unconventional!), and sent one of them on a route equivalent-seeming to Route E, which looks sensible to me, but the other one is going to the west target starting out at (up to the last hex) the same route (so, super long route), and is a Dhow cutting through Kraken territory, which looks not so sensible.

Look at Merfolk donut only, check to see if that affects merfolk stats

Look to see if expected damage can reasonably account for observed losses, check where excess losses are occuring (is Jemist right that there are unexpected losses?)

check to see if Captains affect anything

check to see if time docked affects anything

check to see if voyage purpose affects anything

As Yonge notes, there are 19 encounters not on the planned route I did not see a pattern and attribute this to noise in the data. Note that it is possible that, even if something was displaced by noise, it would still end up on the planned route. I am inclined to attribute the Merfolk event on O5 to such noise, the event probably having really occurred on N5, which was also on the ship's route.

• Take The Bloody Diamond to L13, Q6-P6-O6-N6-M7-M8-L8-K9-K10-K11-L12-L13, then (hopefully) back the same way.

(I thought about a detour to avoid whatever's (not?) going on in L12, but decided it's probably fine.)

• Take The Orange Falcon to E8, Q6-P6-O6-N6-M5-L5-K5-J5-I5-H5-G5-F5-F6-E7-E8, then (hopefully) back the same way.

(I considered alternate routes that punch through F8 and G8 while avoiding icebergs, but decided to gamble that E7 isn't a Kraken hex.)

• Pirates, Storms, Sharks and Harpies seem to be everywhere; no way to avoid these, save making your journey as short as possible. (ditto Dragons, probably, but they're rare enough that it's hard to say for sure)
• Reefs are in every sea hex adjacent to land, except for some adjacent to the ports.
• Icebergs are more common further north.
• Merfolk have a territory in the centre of the map, and another in the southwest.
• Kraken have very specific hunting grounds, which my routes go to great lengths to avoid.
• WMF occurs almost exclusively in hexes adjacent to Q1 and J8. Dragons and/or Wizards on the islands?

• Barquentines and Dhows have 20HP; Carracks and Galleons have 30HP. The effects of attacks are denominated in these hitpoints, so it's worth converting percentages to them.
• Dhows and Carracks handle encounters with living enemies (except Sharks, for some reason) much worse than Barquentines and Galleons.
• I'm pretty sure that a Galleon is just a 30HP Barquentine, and a Carrack is just a 30HP Dhow.
• As a general rule, Galleon>Barquentine>Carrack>Dhow. All apparent evidence to the contrary is because the Admirality know Dhows are terrible and keep giving them easy jobs.
• The Admirality really don't like sending ships out unless they've spent at least five weeks docked; they do this so rarely that I don't have enough data to infer whether the prohibition makes sense.

• This scenario is dice-based, as can be seen from the distributions of some of the simpler encounters: icebergs do 1d6 damage, sharks do min(2d4)-1, harpies do 1d6-2 or 1d6-4 depending on ship type.
• Merfolk seem to do zero damage exactly half the time. If I had more time I'd investigate what this means.
• Pirates never do exactly 1HP damage. I suspect that - when they damage ships at all - their damage is calculated from "roll XdY, pick the two lowest".

• Both ships are heading to Kraken territory; I don't think this is a coincidence. I suspect their 'cargo' is either sacrifices or explosives.
• There's exactly one Carrack that claims to have taken 5% damage, which should be impossible. Did its' captain lie?
• It's suspicious that L12 is so rarely visited, especially when the Kraken-infested hexes to the south are so popular. My fear that it houses a history-eating monster which causes visiting ships to never have existed is *almost* certainly ill-founded; more likely, it's just the one hex in the Admirality's waters that's not obviously on the way to anywhere.

I couldn't find much just by looking at the data.
 
Roughly 90 percent of all type of ship survive their voyage.
Survival rate for different purposes varies between 84 and 92 percent doesn't seem partcularly significant
 
Looking at the survival rates for different combinations of ships and purposes revelas some anomalously low values Carrack carrying redstones only 79%. Dhow and Mythrill 71% are the standouts. Might be a statistical fluctuation, and as we don't know what we're carrying it doesn't help much
 
Ships that sail only one week after their last voyage have a noticeably lower survival rate (74%), otherwise it doesn't appear to have much effect. So provisionally ignore all possible ships that sailed one week ago.
 
Voyages of length 10 or less have approximately the same survival rate of 90 percent, but this falls to 79% and 76% for voyages of length 13 and 14 respectively.

There are 19 encounters that did not take place on the planned route, and one of them occurred on land. This is a small fraction of the total, and they all occurred close to the route suggesting the planned route is reasonably reliable.
 
iceberg encounters are concentrated in the N part of the map, and are more prevelant during the N hemisphere winter.
Kraken encounters seem to be restricted to a small number of tiles which tend to come in clusters, they are slightly more active during the summer. 
Reef encounters seem to be restricted to a small number of tiles which tend to come in clusters. 
Merfolk seem to be restricted to a few moderatly big clusters
Wyrd Majick Fyre is centered on a cluster around J8, with a few random encounters elsewhere. Given the small number there is no reason to think these tiles are any more likely to suffer an encounter from it than any other.

Finding paths which yield the minimum expected damage (defined as all damage done in known encounters on route + 100/hexes on route for all planned routes that went through it but got destroyed yields the following)
Best path to first destination(L13) is:
(1) Q6 P7 P8 P9 P10 O11 N11 N12 M13 L13 
Best path to second destination(E8) is
(2)Q6 P6 O6 N6 M5 L5 K5 K6 J6 I6 H7 H8 G8 F8 E8 
 
Restricting it just to voyages leaving in June leads to::
Best path to first destination(L13) is
(3) Q6 P6 O6 N6 M7 M8 L8 K9 K10 K11 L12 L13 
Best path to second destination(E8) is
(4) Q6 P6 O6 N6 M5 L5 K5 K6 J6 I6 H5 G5 G6 F7 F8 E8
The slightly more northerly route in (4) is possibly because icebergs are less prevalent at that time of year, and they are concentrated in the northern part of the map, however there is no data at the end of the route, and Kraken have been seen in these hexes at other times, and they are more active than normal at this time of year, however the southern route also goes through Kraken infested waters.
  
Assigning double the weight to destroyed ships (and counting all voyages) yielded route Q6 P6 O6 N6 M7 M8 L9 L10 K11 L12 L13 and route (2) again. So this looks reasonably robust against changes to this weighting.
  
  For the captains choosing those that have survived more voyages than any other seemed like a reasonable first guess, however looking at the data suggests that the same name can be given to > one captain e.g Seamus Reagans voyages occur in 2 widely separated groups. So instead we need to look at the ships, which can hopefully be uniquely identified by their ids. Ships are generally commanded by the same captain. The 2 ships that have survived the most voyages are the Orange Falcon followed by the Mopey Diamond.
  
So my provisional answer (Which may be changed if I get time to look into this further) is:
Send The Mopey Diamond, a Carrack captained by Conall MacDougal by route Q6 P6 O6 N6 M5 L5 K5 K6 J6 I6 H7 H8 G9 G10 F10 E9 E8
Send The Orange Falcon, a Galleon captained by Brandon Buchanan by route  Q6 P7 P8 P9 P10 O11 N11 N12 M13 L13

voyage 3352 has a storm encounter at P14, which is a land hex