Back during WW II, when Dad was off to war and meat was rationed, we raised rabbits. It fell to me, the oldest child, to kill and dress them. The way to do it is grab the hind legs in your left hand (assuming you're right handed), put your right hand around the head with your thumb on the back of the neck, and stretch the rabbit's neck to stun it. Then take a hammer-handle and whack it behind the head to break the neck. Hang it by a hook though the joint in a hind leg and cut the head off. Cut off the front paws, then cut the pelt around the hind legs. The pelt can then be pulled off. Then cut open the abdominal cavity and clean out the lungs, heart and intestines. At that point turn it over to Mother to wash, cut up and cook.
You've got it right!
My mother wouldn't allow any game into her kitchen unless it looked like it came from the store!
Not that she (nor my sisters) couldn't handle the chore herself, but it was part of the process of turning me into a man!