https://www.healthline.com/health/mange-in-humans
Yes mange is transmittable to humans. But with a little precaution I'd say the risk is very low to none.
If I shoot an infected yote I won't touch it. I loop a rope around it's leg and drag it into the bush leaving the yote and the rope behind. If I don't have a rope I only move the yote if I have gloves and I also toss the gloves. I don't even bring the gloves home with me.
As long as you limit your exposure and wash your hands thoroughly asap the risk factor isn't high enough to worry about.