If we’re talking about just one ship in a sea zone carrying just one or two units, there’s not much potential for confusion. If we’re dealing with a situation in which a large number of transports in a single sea zone are carrying a large number of units, the simplest solution would be to keep all the transported units physically off the board and to represent their presence on the board via one or more markers. This is basically the principle of the task force markers that were used in the original A&A Pacific game.
There would be two basic approaches. If you consider the transported units to be a single group, all you need to do is plunk the sculpts into a pile off the board and to put a small marker – anything would do – next to the group of ships transporting them. If, on the other hand, you want to track in detail which-unit-is-aboard-what-ship (so you can figure out what troops and equipment get lost when ship X gets topedoed, for instance), then you’d need to put a little numbered (or lettered) marker next to (or under) each ship, and a corresponding marker off the board next to each unit or pair of units being transported. Scrabble tiles could be pressed into service in that role, as one possible quick-and-dirty solution. For a more elegant, you could use HBG’s cardboard naval task force markers, of which it has a wide selection.
In any case, this would fix the transportation problem without having to replace the ships themselves (or until replacement ships become available, if you want to look at it that way).