No plates without 3rd party liability insurance (except certain temporary ones but that’s not what you’re after anyways).
The insurance will inform the authorities directly if they have made a binding offer, which enables you to collect the new plates if you have the old grey card with you. By doing so you accept the offer, it’s as if you’d signed the contract.
See here for Kanton Zürich , Fahrzeug mit neuen Kontrollschildern einlösen.
Be careful, he has your money and also title of ownership of the car in his hands, what guarantees do you have.
If you trust the guy then no problem
If you don't,
1)Make sure you have letter from leasing company stating they will remove the clsause about no reselling from the grey card once the agreed amount has been paid.
2) Go to bank with him and pay off the leasing company directly without passing via his account, pay him the difference, if their is any. If more is needed to pay off lease, make sure he pays his part FIRST
3) Keep hold of the grey card, go to Auto services and make necessary changes. It will take leasing company a few days to "release" the car.
Done!
Tom