There are various ways to keep sausages succulent without using huge amounts of fat.
That wiener recipe is fascinating though. No rusk, or rusk substitute and powdered milk ?
Also they are smoked then steamed. I always though that hotdogs were steamed/boiled first then smoked (I've tried both steaming and boiling and boiling is much less hassle).
It's a good spice mix - I'd probably use smoked paprika instead of the regular vanilla variety and I like coriander, so that's a given.
Be interested to see pictures of the finished product.
I certainly would not add a lot of extra fat to the mix. If you're using spring venison then you will need to use moderately fatty pork, but autumn deer tend to be plenty fatty enough on their own. I like to keep my fat content for sausages down to below 10 %. Tastes better, cooks better, is better for you. Commercial wieners are around the 30% mark. why ? Fat is cheap - that's it really.
I always use oats in my sausage mixes, soaks up the moisture and helps keep the mixture succulent. Also healthier than plain rusk.
As to mincing versus chopping in a food processor. I'd do either one or the other. I tend to use a coarse mincing plate and mince twice for sausages and use the food processor for burgers and grills. I find that you lose a lot less moisture when cooking with a chopped meat as opposed to minced.
Mincing is quicker for large amounts and sausages are contained in skins so less fluid escapes during cooking (Ibelieve it's the compression of the meat during mincing that makes the difference).
For wieners I'd probably be inclined to use the food processor only and chop the living crap out of the meat. get it down to pate texture. That way when you cook it it'll have that homogenous commercial sausage texture. But with decent ingredients and seasoning.