Can’t say I’ve done it, but I imagine the problem is that if your
wax is soft enough to press in a good fingerprint, then the wax
sticks to the finger enough so the impression gets messed up. Is
that about right?
I’d try with a soft red 'boxing wax", worked as a kneaded lump till
quite soft, and then press the finger into that. But use some sort of
separating agent. Not sure which of these would work better, but I’d
try either spraying a bit of silicone mold release spray on the
finger, or on the lump of wax, or both, before pressing, or perhaps
dusting a good layer of cornstarch or baby powder (same thing) on
both the wax and the finger before pressing. blow off excess powder
before pressing, so it doesn’t mar the image.
If that doesn’t work, a separating agent that has worked for
pressing harder things into wax, is saran wrap. But for very fine
details like a fingerprint, I’d bet that would get in the way.
Also, before giving up on what you get, cast the thing. In the wax,
I’ll bet the pattern doesn’t look as sharp and crisp as it will once
cast in metal. Consider, after all, how smooth a nicely filed carving
wax model can look before casting, but after casting, the texture left
on the wax by the file, which looked quite smooth in the wax, is much
more apparent on the metal.