I would confirm the official cancellation policy. I think it's 48 hours, but might be 24. It's because of late cancellations (and because people want their money refunded) that you might be able to get lucky and sneak in there a day or 2 before your date. Another approach - if you're there at the pool, check with the cabana attendant that morning that you want to rent the cabana - there might be a day-of no-show. Or keep calling the PLAY line and ask a couple times each week to see if something opens - never hurts!
The problem at BC/YC is there are only 4 of them (at least there were 4 before the 6-month refurb - I don't know if that's changed), so they are extremely tough to get. Good luck - hope it works out for you!