Betelgeusians don't have wings. One is visible full-length on the balcony in the TMP rec deck scene, toward screen right in a brown uniform. (TrekCore doesn't allow direct image links, but if you go to their HD gallery of TMP screencaps, Chapter 9 - Mission Briefing
, you can see him in image 552, the tenth image in that chapter.) He clearly has a normal humanoid body plan.
As I understand it, the running gag behind Vilix'pran was to represent a distinctly nonhumanoid alien, something they couldn't afford to depict onscreen with an actor in makeup, so we'd just keep hearing descriptions of this really alien being that got more bizarre each time. Something as humanoid as a Betelgeusian just wouldn't be in that spirit, I think.