I can try the dog shampoo because they are usually not moving to much by the time I am ready to do the cleaning.
Tin snips and a sharp knife. Cut the feet off with tin snips. cut their head off. Cut under the tail along the back. Work the skin loose around the legs and arse. Hold by the tail and pull. Should be able to do it in less than 2 min.
Make sure they're dead before sticking them in your pouch !