Well it's my first time posting here, feel free to flame away if that's common knowledge/has already been posted somewhere on the forum.
1) Go to your profession tab (P > Professions), grab your [Skinning] ability and put it somewhere on your hotbar.
2) Disable autoloot.
3) Kill some monster your can skin and loot it.
4) Target the corpse and use your [Skinning] ability over and over.
Can do it semi afk, mob will despawn eventually but you can get another one and spam your key on the new one.
Tried on grey mob and it works as well, so I guess you can make a new char, learn skinning and get to work.