Get them involved in every step, from preparing the traps, to scouting for fur, to running the traps, to skinning the animals. I have met some people that feel kids shouldn't be around this. It is natural, clean fun. It helps to teach the kids responsibility, that hard work will bring results and a love for the outdoors. Most people learn by actually doing things with their hands.
Kids are the same way.
Besides, they will have no prejudices taught to them that skinning and cleaning animals is gross. Not unless you have taught them that. Tell them the first coon is for their very own hat. If they are too small to set the trap, have them place the bait and the lure. Especially on the bucket set.