I just brought a mule deer cape and antlers back from Wyoming. We caped it and sawed the skull plate off. I cleaned most of the flesh off the skull plate, put a garbage bag over the skull plate and duct taped it to the antlers, I also layed it out in the sun to dry out before I put the garbage bag on it, trying to keep the smell down. Took it to the UPS store and told them to box it and ship it to me. Cost $80.
I purchased a cheap cooler at K-Mart put the cape in a garbage bag in the cooler with 8 lb of dry ice on it. By the time I got on the airplane the dry ice was gone and the cape was mostly frozen, it wasn't fleshed or salted, that isn't necessary if it's frozen, let your taxidermist deal with that later. Put some duct tape around the cooler so it wouldn't come open and checked it as luggage at the airport.
I now took a duffle bag full of gear, clothes, etc and shipped it home UPS. Cost $100.
I didn't save much with UPS, a third and 4th bag would have been $125 each on the plane but I was by myself and I didn't want to deal with all that luggage at the airport.