Hello, I really wouldn't recommend letting him do it his way! He went into the back of you, therefore it is entirely his fault, no dispute there.
I had a similar situation a few years ago. A valet company were cleaning my car at my workplace, miles away from my home. They crashed my car somehow. The guy who owns the company offered to sort it out himself, as he owns garages as well. I knew him vaguely, he did a lot of work for my company, so it seemed like the easiest option to let him sort it out. I called my insurance company to ask if it would invalidate my insurance, they said it would be ok.
So, he gave me money for a hire car and took my car away. Got it back a week later and took it to my garage to check it, they said it was still messed up, hadn't been fixed properly at all. I called my insurance and they washed their hands of me, saying that because I had let him fix it, they were no longer liable. I went a bit mad at them, they came out with all manner of excuses to not help me out.
Eventually I decided to let the valet guy take it again to repair it properly, against my better judgement. It was the only way to get it fixed at that point. It came back a bit better, and it was deemed to be roadworthy by my garage and I sold it, couldn't bear to look at it after all that!
The lesson I learned - just go through the insurance, unless maybe it's a wing mirror or something. If you don't even know the extent of the damage yet, don't agree to anything. He has no choice regarding you informing your insurance and letting them sort it out for you. Whether he chooses to foot the bill at his end or let his insurance pay it is up to him and nothing to do with you.
You're asking for trouble if you let him sort it privately!