I often use the following recipe for pork butt. It comes out really tasty. Though there is a significant amount of fat in a pork butt, this recipe does not result in the grease dripping chorizo that you get in the grocery stores. I usually have to add some butter to the pan to provide some 'juice' to mix into the scrambled eggs that I cook with it.
I'm not sure how it will work with lean venison. Perhaps you can modify it to fit your needs. Good luck.
G-Man's Pork Chorizo:
1 lb pork (25% fat)
1/2 tsp dried oregano
1 tsp salt
1/4 tsp black pepper
1/2 tsp garlic powder
3 TBSP chili powder
2 tsp comino
1 TBSP vinegar
Note: Boston butt pork is about 25% fat. Leave the inter-muscle fat with the meat, but trim the outer layer of fat, if desired, to reduce fat content.
Cut the pork into 3/4" cubes. Season the cubes with all the wet and dry ingredients. Pass through the coarse plated grinder. Pass 3/4 of the ground meat through the grinder a second time. Mix all ground meat together. Roll into 'tubes' of plastic wrap. Allow one to three days in the refrigerator for the spices to get friendly. Freeze whatever you don't plan to eat within about a week.
*edited to correct formatting errors