Well, most naval battles of the Medieval ages were rails on ports to destroy or seize an enemy fleet. You're pretty unlikely to have a pitched battle in the middle of the north sea.
Imagine transport ships just as normal ships that are temporarily seized to move large numbers of soldiers. Warships would make more sense as a retinue, making them more valuable and requiring of protection. Warships would move much faster than transports and will destroy them quite easily, they would be able to carry a small number of soldiers, but probably only enough for raiding.
For warships they'd probably have to add a small stretch of coastal water and a new mechanic for landing anywhere hostile or without a port. You could have important ports represented by a small sea tile next to the coast. Your warships would be here and would take no attrition and be reinforced. If it was a retinue then you can put an admiral in charge, most like from a vassal republic otherwise you'd have to use a decision "Invite admiral to the realm" who gets the trait "Ship Captain" allowing him to be an admiral.
You can use your galleys to raid the ports, destroying their ships to allow you to land safely. Alternatively for defense, the warships could have a patrol path that you set. Pitched battles would only be in coastal waters.
