All you have to do is activate them in your inventory and they are added to your custom skins and no longer in your inventory. If you sell them, you don't have access to them because they were still an item and not..what's the word...'bound' to you?
To kind of answer your question, the skins do show up in machines and as drops again. I have never sold a skin and seen the same one pop up in a machine or as a drop later. In fact, I have never sold a skin I didn't already have unlocked. But I have seen skins that I already have unlocked pop up for sale or drop a second or even third time.