That's how I do it. I do use mole grips when skinning munties though as the skin hangs on a bit more that it does on other deer. Skinning this way certainly saves a lot of hair getting on the meat as the fur is below the exposed flesh so any loose hair drops to the floor.
The important bit is right at the start. You must cut the front legs off at the bottom joint or the carcass will fall on the floor when you start pulling on the fur.