Can you give your dog a "Chuck-It" swim toy to hold in his mouth while he swims? That way he'll have something in his mouth so he won't bite your arm and the toy floats https://www.amazon.com/Chuckit-Amphibious-Bumper-Assorted-Colors/dp/B001AQZ4FE/ref=sr_1_2?keywords=swimming%2Bdog%2Btoy&qid=1659225764&sr=8-2&th=1