your rate will not go up since it is "not-at-fault".
if u do agree to let the other person pay with cash, make sure he/she is aware that you are going to take your car to the body shop of your choice and the car must be fixed completely to your satisfaction first. and they must also pay to cover the cost of a rental car while your car is in the shop too.
if u do agree to let the other person pay with cash, also make sure to write up a contract that he/she states it is their fault and both parties have decided to settle it with a cash payment of $xxxx. then have a photocopy of their drivers license and both of you sign it.


its just easier if everyone goes through insurance. especially since both of you have the same carrier.