No risks. Just easier to move the deer.
The mountains I hunt in are true back-country wilderness, so you can't hunt from a road or trail. Miles upon miles of hiking in... up mountains, down valleys. I absolutely love it because I get far enough in that I'm the only one out there where the deer and elk play.
I prefer to gut the deer where it falls because I don't like dragging that weight back out with me. I don't know how much the guts of a muley weighs, but I'd guess 50-80 pounds depending on the animal? I know an elk's guts can weigh upwards of 100 pounds or more, depending on the time of day (after/before feeding).
You might be hunting close to roads or with horses, if so, it's simpler for ya to do it your way. However, if I did shoot a deer in an easily accessible area, I'd still gut on site because I don't want to have to dispose of the guts
at home or wherever. Coyotes gotta eat too.
Doing it later, as you do, isn't going to harm the meat at all unless you shot them through the guts. When that happens, their digestive juices get loose and begin to 'digest' their meat, and that will definitely spoil the venison. Also, deer in the field see other dead deer and their remains all the time, so it doesn't bother them.
I even heard a hunter tell a story about shooting a deer and gutting it. The next day, they go back out there and find another deer eating the stomach contents out of the gut pile.
So that should tell plenty.