You are in a slack time. You should have no trouble getting a ball anywhere but Cooper and perhaps great harbor on Friday or Saturday. Little harbor next door always has balls. Arrive at Cooper by about 1 pm and you should find a open ball. Keep in mind that you should be comfortable anchoring to skipper a bareboat. If not perhaps have a skipper put on the boat for a day or two and practice. I have come adrift twice in the BVI at night. Both times I was on a ball.
G