Transferring personal registration

Hi guys I'm getting a bit confused with what to do here.

I'm swapping cars with my dad, and I have a personal plate which I'd want to move from the Skoda to the Mercedes and I'm trying to figure out the best way to go about it.

If I swap car first and then move the number plate, we'd both have to pay extra fees, first for changing car as I'm getting a higher powered car, and then again about a week or so later for the admin of swapping registration plates on the policy.

If I'm right in thinking so, could I get the plate transferred, and as soon as the plates are swapped over, ring the insurance and then reinsure the car in my name? The only issue I can see is that I'd have to wait for the V5c to come through, and then we'd both have to send off the new keeper supplements.