Well, it could be a national units with a limit less than three. There is no reason you couldn't set its limit at 1 without making it a world unit. Each civ could hve 1, but replace it if destroyed.
Since the it would require a minimum level and since ships don't gain xp automatically like arcane units do, it is unlikely that anyone would actually manage to get 3. It might be a little more unbalancing if it were just made a hero, at least it if works the way most heroes now do, since only one player could build one wand there wouldn't be the level requirement.
I'm not sure that you could program it to need to end its turn on water, but you could probably make an event that causes it to crash if it ends its turn on land. Or you could make its flying promotion only temporary and give it a spell that gives it flying again. Or you could forgo the unit altogether and make a spell that grants any ship a temporary flying promotion ( but I believe Kael said, when talking about water walking, that the AI wouldn't be able to understand how to use this)
Edit: Unfortunately, I'm not sure the flying ship idea will work. I went ahead and added one on my own, which seemed to work fine until I tried crossing over land with passengers. If you try moving the boat directly on to a land tile, it assumes that you are trying to unload. It never seems to let you move the ship directly onto a land tile, but sometimes it works fine if you try to move it a few tiles inland at the same time. Also, the land ice terrain seems to be impassible to the flying ships, although it is passable to land units and no other terrain is impassible to any flying unit.