Sounds like a chef problem. Presumably the beasts belong to your boss anyway, and I'd have thought any chef worth their salt ought to be able to do it. The management of the hotel should know the answer, and be responsible for ensuring the legal origin of the food they acquire and sell. I'd be inclined to wash my hands of the business and just let the hotel and boss collect anything they want.
I see you are in Scotland mate, all venison must pass through a venison dealer before it can be sold to the public
So either you your boss or his chef needs to be a registered venison dealer or have them processed by a registered venison dealer.