Often you can tell chronic wasting disease from the looks of the animal before you take it. However, on a stripped carcass that would not be the case. Some scientists now think that the species barrier can offer some protection from it. All in all, while some people have succumbed to it, it can be rather rare.
Myself, I'm actually more concerned with parasites and bacteria than prions.
A lot of it depends upon your area of operations. For example, there is an advantage enjoyed by the folks way up north in places like Ontario and British Columbia. Game lasts a while when you harvest it inside a refrigerator. The extreme cold also does a good job of killing off many parasites and a wide variety of insects in general.
Here in the coastal bend region of southern Texas, we are at about the same latitude as New Delhi, India, and southern Algeria. We have snow about one day every 12 years or so (we had snow one day this past December 2017 and our previous snow was one day in December 2005). Our winter is normally like an Ontario spring, maybe a bit warmer.
This semi-tropical environment much of the year does mean we have a staggering abundance of game (alligators, deer, ducks, wild hogs, javelina, etc). However, it also makes parasites in game and insects in general a special issue that does take some getting used to dealing with (oh yes, and the snakes). Also, when you harvest game, you want to get the body cavity as cool as possible as fast as possible. That is a lot easier to do in places like Ontario than here.