...Sorry if that came across as rude at all, sleep deprivation is my equivalent of drunk-posting. Anyway, I think it originated in Underworld. I've attempted to find the origin multiple times, and each attempt fails to go back any farther than Underworld, which is exactly the kind of movie that would invent a term like that. I didn't dislike the movie, but it was very much an edgy "modernized" take on vampires and werewolves (complete with stuff like UV grenades), and shortening lycanthrope into a snappy nickname is on-brand for that sort of thing. Seeing it get used in the Castlevania reboot, a series which is supposed to be rooted in classical monster movies... Well, don't even get me started on that game.
I've always liked the full "lycanthrope" myself, probably because it sounds like a scientific classification, with "werewolf" being the common vernacular and "wolfman" being a casual nickname. (The fun part is that all three of those words mean pretty much the same thing.) On a mostly unrelated tangent, I've also recently been spurred into debates about D&D using the term "lycanthrope" to describe non-wolf were-creatures. "Now hold on a second, DM. 'Lykos' means wolf, and 'anthropos' means human. That were-rat is a... Hang on, lemme Google this..." "Oh my God, just roll for initiative." "Wait, hang on... I think it would be... Mys?" "Misanthrope is already a word. The were-rat bites you and you die." "Alright, fine. But it was a zoanthrope that killed me, not a lycanthrope!"