You should consider skinning. I have and do skin for those who want a beaver or whatever skinned during the open season, but its not that often. Charge what you need to. Many times the customer will offer to pay as they know it is extra work. You can just charge what a hide is bringing, but if you are charging a lot for the job, I sometimes throw it in. One client had a coat made from the beaver. We supplied him a few additional beaver to make it enough with the 50 pounder the center of it.
Once you catch an animal and get payed for it, if the season is open there is money to be made putting up fur if you have time. I can put up two blanket beaver in an hour without too much trouble and if they are bringing even $25 each that's 50 bucks for the hour which isn't bad money. Like to keep my hand in, not do a lot, just a few. Timed 3 mediums a while back, skinned, scraped and tacked them in 51 minutes, again they are free at that point, something to do after hours. Even roughing them out and selling green works. Still like handling fur when its prime. Only thing, I seem to be worse as knife sharpening. Used to time ourselves, Mickey and me in Virginia to get through them fast. Did a blanket in 2 min 42 but saw one done in a video in 2 min 24, something to shoot for.