I’ve been doing healthcare in Canada for 14 years, and “cathing” has always been the norm in the places I’ve worked. Even in professional manuals, they would usually use “catheterizing” in the formal introduction to procedures, but “cathing” for employee guidelines. I doubt I came across more than 15% of staff who would use anything else, and even then it would be split betweeen “catheterizing” and “cathetering”. I worked in home-based health support, which is less formal than hospital settings, but when I was working with clients in-hospital the doctors and nurses would generally use “cath”, “cathed”, and “cathing” when we were talking informally.

So it seems that medical staff use cath amongst themselves. Probably patients who use catheters regularly have learned the in-usage themselves.