Tweety's brother used to have (still may have, not sure) a boat kept in St Marteen, with a crew of 2, that he rented out.
On one port visit while on a cruise Tweety arranged for the boat for the day, and we went sailing. It was a fabulous day, and they made us a delicious lunch onboard as well.
To do it for a full week, you'd have to really LIKE sailing. I don't think I could take being bounced around that much for a full week