Chavtasticness of “cherished” number plates aside, does anyone know if I could take a private plate off a car onto retention document and replace with a different private plate at the same time? Or do I need to wait for the V5 to arrive with the original number plate before I can swap to the new one?

Trying to avoid having to update the insurance details twice, and the plate being removed is most definitely worth a bob or two so may as well sell it rather than losing it back to DVLA with just a straight swap.