If the damage is minor, you may be able to leave the insurance out of the equation. However, it’s best to get an estimate for damages from a body shop before you allow the other driver to give you money. Sometimes there may be damage that you didn’t see, and it could be more expensive than you think to fix it.
I recommend always letting your insurance company know of the accident. By going through them, you won’t have to haggle with the body shop to get the work done; that’s what the insurance is for. Make sure you’re always covering all your bases because if there’s more damage to the car, your insurance company won’t help out if there isn’t a claim to match up with the damage.