Yep you have to use transmutation stones. It’s pretty easy to use. Basically once you use the stone, a window pops up and asks you to drag two items in it. Once you do, you have three options. The first one, is the skin, just click on whichever one you want to have. The second is the stats, choose the one with better stats (obviously), and the third option will be the rune you want to have, if either of the items have a rune on it already.
So yes, your two items are kind of merged into one, and yes, the resulting skin is re-usable.