Like others have mentioned, Coinbase might be a good way to go as they don't require ID for using them as a wallet, just don't keep too much BTC there. You can also consider using a gambling site (<-- Not Recommend) like NitrogenSports or DirectBet's gambling wallet as they don't charge fees for withdraws. Might not make a good impression on the sites running it however, and they might limit your account/ban you.
You know I heard coinbase is going to do anything, moreover coinbase regularly keeps your transaction in check and once they found a gambling or any activity they block accounts, someone mentioned that in one of the threads earlier.
I think the best one to use right now is : rushwallet ( but at your own risk ).