The earliest reference I know about is
Wendt, H. Die gordische Auflösung von Knoten. Math. Z. 42, 680–696 (1937)
It's been a very long time since I read this paper (and my German is mediocre, so it would take some effort for me to re-read it today), so I can't remember if it references anything else.
As evidence that this is the original source, Reidemeister's classic book on the subject references Wendt's paper when it introduces the unknotting number. See the beginning of Chapter 2.