Sell a car privately in Germany - when to unregister the car ?

Guten Tag,

So it looks like I just bought a car in a dealership. The Kaufvertrag is signed and I therefore have all the car papers I need in order to register and insure it before I go back to the Autohaus to actually get the car. They told me they could keep the car for a few days until I get all the paperwork done.

In parallel, I am trying to privately sell my old car and am starting just now to see interested parties contacting me. It is very likely that I'm gonna need to register/insure the new car before I'm able to sell the old one. After asking around and reading most of the threads on this topic, I understand I am left with different options...

1. Unregister the old car (and therefore terminate the insurance contract) before selling it and transferring the license plate to the new car. Keeping the same license plate number actually matters for me. I have an underground garage I could leave the car while it is unregistered not to have it out in the streets. But apart from asking the potential buyer to show up with red plates or register the car before, I am not sure how to proceed nor whether it is a good idea to hand over the Zulassungsbescheinigung Teil II so that the buyer can register and insure the car himself before driving home.

2. Keep the old car registered until the sale, and go to the Zulassungsstelle unregister the car with the buyer on the day the sale takes place. That would mean I'd need to have temporarly 2 cars registered under my name, all this to unregister my old car as soon as I sale it and be left with a useless spare of license plates. This doesn't sound ideal for me but it looks like privately buying a car which is still registered and insured is usually the preferred way in Germany.

Of course, the best option for me would be to sell the old car and then directly register the new car and go pick it up, but timewise it might not be possible to do it in this order.

Does anyone have past experience there or any advice on how to proceed ?