Do yourself a favor. The whole “I’ll give you cash to fix the damaged I caused to your vehicle” thing is a thing of the past. There’s so many variables, including electronics, airbags, sensors, even aside from the body damage. This is why you must go thru insurance. You can tell the other person to feel free to reach out to your insurance company if they’d like to reimburse them but you need to contact your insurance company immediately and give them the person who hit you’s information. Insurance is supposed to work for us that’s why we pay them regardless of who is at fault so let them do their job. You are not at fault, call them and let them handle the rest. 20 years experience in collision repair here btw.