Gassing is more common - if you think about the ease of gassing animals in cages, versus trying to hold the animal whilst inserting a metal probe into its anus, it doesn't actually make much sense.
I don't think anyone can defend the Chinese fur trade, but European fur is much more humanely fared, certainly much gentler than much of the meat food trade.
It's also a myth that the carcasses are just thrown away, they go into pet and animal food.