Get the a/c. Then you at least have the option. I can't imagine not having a/c in June in the BVIs. You can't get away from the heat otherwise.

At least being able to sleep comfortably at night is a winner. You also don't have to do the hatch dance.

This past February we had a/c and ran it every night. We don't like the muggy feel or the hatch dance. Plus, the white noise is nice when traveling with other couples.