I used to walk a couple Newfoundlands for a friend (one at a time).
They were huuuuge dogs and I could not control them with my hands, so I had a sturdy leather belt that I wore around my waist and attached the leash to.
Do you have a yard you can play in with him? Grab a ball or a stick, throw it with your good hand.
Play 'tag'. My golden used to love playing tag where I'd chase him around. It'd get both of you running and burn calories without using the hand.
Is there someplace nearby that you can take him... woods, beach, etc where he doesn't need a leash?