Sorry for the lateness of the reply!
Anyway, drilling a hole in the hull? Wooden ships are notoriously able to float, drilling through a thick hull to open up a large enough hole to let enough water in without arousing suspicion seems an impossible task to me (especially if you have swam a great distance to just get there). They seem so small as ships, so much noise would be very noticeable. Some military ships had very low gun ports close to the water line, that in heavy seas could let enough water in to capsize the vessel (Mary Rose I'm looking at you), so potentially you could use them somehow. But that's a big military ship, not a merchant cog, and in calm waters it would be no help. And no, I have not heard of medieval 'combat divers'!
Explosives? If it were a military vessel, and they were using canons, one could potentially rig the "powder room". There should be potentially enough there to fundamentally damage the structure of the ship and cause secondary fires. If canons on ships (or that ship) is not your thing in-universe, getting enough 'expolosive' onto the ship to actually cause enough damage seems implausable via swimming. Even alchemical wonder weapons. (Unless it was transporting this as a cargo...but it would surely be under close guard and scrutiny, given how dangerous it was to carry.)
You could potentially put in some sort of 'alchemical' bomb, as you say, and just give it enough magical properties that gives it a massive explosive/intense fire property, but that feels like a cop-out. White Phosphorous may be one potential subtance - see:
White phosphorus munitions - Wikipedia - properly prepared has an inbuild 'timer' - see the history bit with carbon disulfide. (But how do prisoners get their hands on pure white phosphorus?)
Personally I might go for fire. Rig the ship to try and have an uncontrollable fire. Wood may float, but ex-trees, pitch, rope and tar etc. are highly flammable. Now, if the ship is near other ships and the fire cannot be fought, the crew themselves and others in the harbour might actively try to move the burning ship as far away from others to limit damage. Of course they would probably try and move the ship to a position that does not hinder the rest of the harbour.
Or they would try and move the other ships away. This seems to make sense to target the ship furthest away from the rest, as 1) you have better chance of capturing the closest ones, 2) it takes enemies away from you dealing with the burning boat (and they are more likely to try and tow that one away, rather than sail the other two?) 3) it needs someone to swim a big distance, which is your scuttler's skill, and to swim back to another ship.
In the confusion that gives the opportunity for the prisoners to board the other ships and take them over (they might try and claim at the start of the action that they are only going to move the other ships to 'safety'). Simultaneosly it would make sense, I feel, to set up fires in warehouses and buildings on land at some point, so that people are occupied with that too. That is something the men could be getting on with as the first ship is causing problems. Also perhaps trying to fool the garrison with a message right at that start that something is happening in the slave camp (or waiting till someone does come with a message saying that loads of slaves have escaped!) - so that men might be sent to see what the problem was, thus reducing the number of dangerous enemies in port.
So including all of the above, I, the would-be scuttler, would then try and board the ship when there were as few people on it, when it was heavily laden with cargo (will aid in overcoming the bouyancy of the wood in the event that the ship takes on lots of water) and attempt to set fire to the ship in such a way that the few people on board could not fight the resultant blaze. Potentially try and smuggle on large amounts of something flammable as it was being loaded with cargo beforehand, or know that they are present - like pitch/oil or even potentially spirits or liquor, as they were first produced, I believe, in the 13th century, so could be used, in sealed containers. They could be smashed open to drench the cargo deck with copious amounts of fammable liquid that would need to be ignited and then make a sharp exit. Oh, this assumes that this is a decked cog, so that one could carry out these activities without being seen by anyone.
That only deals with one ship though, and I find it unlikely that one sabateur could successully destroy two ships without limpet mines stuffed with copious amounts of high-explosive with (at least) clockwork timers
. Thus perhaps the men could disable the second ship (chopping/damaging the masts and leaving more fire to destroy sails and rigging, or damage the tiller/rudder system?), while then all converging on the final ship and escaping.
It's messy, I know, and quite intricate. Perhaps cut the number of ships from 3 to 2?
