I don't have a complete answer, but here are some thoughts. You might want to look into an Ocean Engineering or Marine Engineering programs. These types of programs would include ship design. MIT has an undergraduate program in Mechanical and Ocean Engineering. The U.S. Merchant Marine Academy has a program in Marine Engineering. A mechanical engineering program would also provide the right type of preparation. In that case, I'd recommend looking at a program with a strong design component in their curriculum. Some of the universities on the coasts may have strong relationships with shipbuilders that result in interesting student projects.
Thank you so much for your questions regarding ship design. This is certainly an exciting field and one that is looking for more engineers!
My suggestion to you is to major in mechanical engineering. You cannot go wrong in choosing that major since it is a broad field that includes so many different topics, including ship design. One of the areas in which you would take numerous classes is fluid mechanics, as you major in mechanical engineering. In that course you learn about the stability of ships; how to best design a ship that requires the least amount of fuel as it is powered through the sea; and how to best design the power source for the ship. I also suggest majoring in mechanical engineering because you can never predict the future of jobs and your likes/dislikes. You cannot go wrong in majoring in mechanical engineering since nearly all companies requiring engineers need mechanical engineers in particular.
I hope that helps and I wish you the best in your career choices.