I don't think it matters that much, just pick one and stick with it. Ship's carpenters sometimes had to do things that neither landbound carpenters nor shipbuilders had to do (e.g. careen a ship in a place with no shipyard facilities to scrape the hull, apply an antifouling compound of tar and sulfur, and calk the seams. But it's generally best to make Profession/Craft skills as broadly applicable as possible. I'd allow someone to use either and set a higher DC on specifically at-sea shipboard carpentry tasks until the character has five ranks in Profession (sailor) to synergize.
I don't think it matters that much, just pick one and stick with it. Ship's carpenters sometimes had to do things that neither landbound carpenters nor shipbuilders had to do (e.g. careen a ship in a place with no shipyard facilities to scrape the hull, apply an antifouling compound of tar and sulfur, and calk the seams. But it's generally best to make Profession/Craft skills as broadly applicable as possible. I'd allow someone to use either and set a higher DC on specifically at-sea shipboard carpentry tasks until the character has five ranks in Profession (sailor) to synergize.
the way i see it is that the skill required would be craft: shipwright with a synergie, as Peruhain said, for five or more ranks in profession sailor, after all a shipwright might never actually set sail on the briney blue...
If you all have Stormwrack you can find very definitive answers and even feats for your main question. There is a section detailing how to use the basic PHB skills for a sea campaign. Without looking at the book, I would have to say that the job of a shipwright would fall under Craft (carpentry) for simply building and repairing ships and Knowledge (architecture and engineering) for actually designing ships. If you had both of these skills, you could easily take Profession (shipwright) and have a bunch of hirelings perform the actual labor for you.