You can do all of it in stages. Skin, and freeze it in water. Thaw it, flesh and wash it, and freeze it in water. Thaw it, dry it, then mount it. You can even dry the skin and freeze it and mount the next day. I would not want to keep a dry skin in my freezer very long. If in water, they can last years on end. No air in the bag and completely submerged.
I always skin, then freeze at least one day in water. I believe the fat tissue fleshes easier. Then I thaw and flesh, wash, and rinse. The skin is then kept in a block of water until the day I mount it. I have mounted birds that were stored for 9 years this way.