That's my point: if CT scans cause cancer, cancer in the wrist or knee should be much more frequent among people who had a wrist or knee CT scan than among the general population. CT scans are relatively new, so there probably is a record in each patient's history.

Again, not necessarily. Different things cause different cancers. You're unlikely to get melanoma from smoking; you're unlikely to get liver cancer from a sunburn.

CTs may not cause significant amounts of wrist/knee cancer - I can't speak either way on that - but that wouldn't mean they're 100% safe elsewhere. For starters, wrist/knee imaging needs less radiation - they're relatively thin parts of the body, and relatively small regions.