What should I do here

Hi, so I was driving to work this morning in the far right lane. The lane next to me, so the second from right lane, was at a dead stop. A man merged into my lane in front of me. I swerved and because I swerved the only parts of our cars that were damaged were the mirrors. He is trying to say it was my fault but to me it’s very clearly his. My question is, should I go through with filing the claim which is a hassle and a headache or should I just cover the cost of repairs for both of our cars to make him leave me alone? Like is the Insurance going to try to say it wasn’t his fault even though it was his fault? Because I’ve had that happen before and the other person totaled my car and I got completely screwed.