Q:
Transmutation of a weapon with skin.
Any time you transmute, you get a choice between the current appearances of the two items you’re placing into the transmutation window. The “old” appearances never enter into the equation, they’re basically gone.
Transmuting, for example, a Jade Dragon Staff and a Krytan Staff, you get the choice between either choosing the Jade staff appearance, or the Krytan Staff appearance. Whatever weapon you applied the Jade skin to originally won’t even be a factor.
So in short, you will be able to transmute your Jade weapon skin to a new weapon using a Transmutation Stone / Crystal just fine.