Odds of Getting In
It seems like just about every smart person on the planet these days is complaining about America's lack of engineers. And while we highly doubt they were specifically referring to ship design and production, the people who do that technically fall under the same umbrella.
The fact of the matter is, engineers (or architects, as the case may be) help us actually make the stuff that we need, so there's generally a solid demand for people who take the time to acquire the specialized education required to do it.
Long story short, if you want to do this thing, you can do this thing. There aren't a whole lot of highly-qualified shipwrights standing in the unemployment line. That said, we weren't kidding about the extensive toolkit of skills you'll need to succeed in this field, so in order to make it, you'll have to have those math, science, and design abilities in ship-shape.