Hi, Adrian...
It takes about two weeks for the tonsil beds to fully heal over. There are a number of types of uvuloplasties (palatoplasty, uvulopalatopharyngoplasty, etc..), so you might ask your surgeon for more specific information about that part, but generally after about two weeks the risk of bleeding drops off.
Bleeding would probably be the most concerning postoperative issue, and the reason to hold off diving for at least that long (if not for an additional week or so for you to feel fully recovered). Bleeding after tonsillectomy is rare in children, but more common in adults. Depending on the type of surgery, this risk may be more or less, so ask your doctor.
Good luck!
Mike