Nope, you can't do it. I think the rules specifically forbid it, but if not it's in the FAQ. (The question has been asked previously.)
Thanks, I don't think I worded the search correctly before posting my own.
Page 8 (right-hand column) of the rules says you can never be without a ship:
You can never be “ship-less” – you must buy a new ship when selling your old one. If that isn’t possible, then you can’t sell your ship.
I appreciate the quick responses from both.
Running some calculations I believe they still won. There was still 10+ gold to purchase a Sloop or Flute during their port action.