As far as I know, it’s the title which is the most necessary. The registration is necessary to drive the car so just make sure to not allow the person to test drive it on public roads (or don’t get caught doing so:)
The registration is tied to you and your license plate number
and that’s not going with the car. The new owner will register it in their own name along with whatever insurance proof is required.
Whenever I’ve bought or sold a car, the registration never figured into the transaction. If you can’t find the title, that will be the big problem.