I guess, this will be a Frame Challenge.
By your description, the dragons seem ill-suited to be good swimmers. They are aerial, not aquatic, unless you have a water friendly type dragons. Just because you use dragons extensively, it doesn't mean they are well suited for every single task. Unless they can float passively in water, their range will depend on their stamina. They are living creatures so need to rest, eat, crap... That's not something you want in your long-range vessels.
Historically ships usually built, because you can move more and heavier cargo over water. Transportation, Logistics. With HUGE dragons around who can fly, it is ill suited for them to be used for pulling boats. It would be way more effective to design a flying vessel around them.
Scenario 1: If your dragons are abundant and easy and cheap to keep, flying vessels will be designed around them with almost no ships whatsoever existing and the technology not refined.
Scenario 2: If your dragons aren't abundant or easy and cheap to keep, wind sailing boats will be the mainstream to cut costs.
The military aspect:
They won't invest in developing dragon pulled ships, because they have no reason to. With dragons, they can maintain air superiority and can easily destroy any dragon pulled ship from high up. It would be an easy target, since the dragon would be restrained to pull the ship. HIGH GROUND rulez!
In case of Scenario 2, they will have a standing Navy, but they won't be dragon powered. They will have Navy supported air force ready near the coasts and if their range is limited, especially for the smaller, more agile dragons, they MAY develop huge Dragon-Carriers, to extend their range of operations. Mostly in huge seas or oceans.
Also, flying create a lot of wind, especially if the creature is huge. It would mess up finely the ship or carriage pulled by such a creature. I imagine there wouldn't be long rows of people wanting to travel that way.
In short, dragon lifted AIR ships? Sure, awesome! Boats? Unless the dragons swim, nope.
Heavy handwavium and Fantasy territory
If you really, really, really want dragon pulled ships, you have to scale it right. With the huge sizes of the dragons in question, it would be the equivalent of oil tankers, huge barges. The dragon would be "high" up in the air with long chains connecting it to the ship. The ship should be huuuuge and/or heavy, to make it practical. Something the dragon can't lift up. Which require a whole lot of fantasy to work and for the ship to not sink. The dragon would function as something like a high altitude sail. This setup would be very slow and would mostly focus on material transport over long distances. Like oil-tankers. Maybe mobile fortresses.
And momentum would still be a bi...!
Scenario 4: (Because we already crossed to significant handwavium territory with the ship's properties)
Dragon-propelled ships, the unconventional way. For this to work, dragons must have the proper wing type (scaly? Not sure) or be an aquatic sub-species of your common dragons. Just like penguins to other birds. Yes, you may have guessed already. The dragons will be partly or fully submerged, with only their heads out of the water. They will use their wings to swim, well row in water.
This would be way more effective than flying, as they don't have to spend energy on keeping themselves afloat. This type of propelling also allow for a whole lot of fantasy possibilities, almost anything goes. The Navy may invest in developing submarines, depending on dragons lung capacity or with only their noses out of the water.