Insurance agent here. Here's what you should do:
1. If you're tired of waiting for the other guy to pay up, call his insurance carrier and report it. They'll have to take a statement from him so be prepared for it to drag on a little longer.
2. If his insurance coverage is cancelled, you can report it to your carrier. You'll have to pay your collision deductible.
The insurance contract says you are required to report a claim to them within a "reasonable amount of time". Your guess is as good as mine as to what that means.

Reporting an incident two or three weeks late isn't going to trigger a cancellation.