If the cohort was to be the actual starship, and get ship captain levels for itself, I'd recommend having it be an android with the Integrated AI flaw.
That way it would pretty much be the ship and still make it work for ship captain's battleship stats.
Being an animated object battleship would have its own stats so it wouldn't get the battleship stats from ship captain. It works, however, if you completely ditch the ship captain class and make an animated object starship. However, that ship will only be as big as the animated object class allows it to be. Plus whatever other size increases you can add to it. The animated object has abilities that allow it to carry creatures aboard so it could effectively work as a starship. Albeit a very small one compared to those a ship captain gets.
Depends on how many people you plan to carry around. If you are to carry around mechas as well, though, you'll likely have to have it be a ship captain.