Selling car properly

Admittedly, it’s my first real car sale and the second one at all. At the first I sold to a car dealer. The car was worth nothing more, I previously registered the car and sold it as scrap. Therefore, my sales experience is de facto zero. Now I want to sell my Daily Driver. It’s not worth anything, but it’s more than scrap. How do you do it right? I want to sell the car logged off anyway. First, for obvious reasons, two Is the following procedure safe and useful? The interested party comes to the inspection, makes a test drive and wants to buy the car. We sign the contract, I unscrew the registration plates and hand over the car, keys and papers. The seller screws short-term registration marks to the car or transports it on the trailer. I drive to the registration office and register the old car and register another car. License plate number of the old car. At the moment you wait several days to weeks for an appointment at the registration office. I.e. the new owner drives my old car while my registration and insurance still existed theoretically and practically, but of course without my license plate number on the car. Can this under any circumstances become a problem for me? For me this looks like the best solution. I just wonder if I am missing something.