For fox, I would cut the catch circle in half by stepping into the circle and the fox would try to go directly away from you and sooner or later he would put the trap between his legs trying to power out. At that point, I would grab it by the tail and pick it up off the ground and grab it by the throat. Then I would pin it to the ground with my knee and while holding onto it's throat, I would grab it by the nose and bend it back over the neck and put alot of force on it till it broke.
Yotes... I would bonk them on the nose with my trappers shovel, stuning them and then I would roll them over on their back... stretch there nose out streight and with the edge of the shovel, I would hit them as hard as I could in the middle of the throat 2 or 3 times. When their legs stuck streight up when you hit them, you knew they were done for.
Did coons the same way but I hit them on top of the head. VERRRY rarely did I ever have a gun in the truck except to shoot skunks. Everything else died by the trapping shovel.
