To settle the argument I would use the pinch collar. Pinch collars with the points filed off are humane. Second, if you are hitting your dog with a hat your dog will associate your hand which holds the hat a threat. This could lead to other problems ie retrives to hand.
Personally I would work the dog in the yard with the pinch collar or better yet an e-collar if you know how to use one. Then if the dog breaks before you command him on the fetch you can let him know who gives the directions come hunting season,