It's going to depend A LOT on the venison.
And the question of is your smoker a "hot" smoker or a smoker with a "cold smoke" capability?
The age of the animal, sex, and what has the animal been eating plays a big part.
Had some venison from a very mature buck who'd been hiding out in a grove of junipers for most of a year...no matter what we tried he tasted like he'd been marinated in Pine sol.
A nice, fat, three year old doe, which had been eating corn, soybeans, and the local suburban landscaping...., was amazing. So you'll have to do an experiment on a small piece first, so see if hickory, oak, cherry, or apple, or even mesquite, work for you. Maybe a combination of two or more?
A "hot" smoker cooks the meat and adds smoked flavor. A "cold" smoker or cold-smoke-capability is what you need if you're going to salt the hams and then smoke and store and age the hams. Same thing if you're going to make smoked bologna or other sausage for long term storage. (smoked cheeses too) Most folks hot smoke the meat, and serve it the same day.
LD