Selling my car before Registration has been transferred?

[Easty-5]

I recently bought a new car. I am in the process of getting my private registration from my old car transferred onto my new car. The problem is that I work away a lot and am rarely home these days. The buyer wants to buy the car ASAP. He lives local so is there anyway I can send away the necessary forms to transfer the reg, sell him the car with the private plates still on and when all the new paperwork comes through, meet up with him, swap plates and give him all the new paperwork?

My other issue is that with my new car, I also need to register it in my name at the same time. I bought the car from a garage and they gave me the V5 (signed by the last owner) but the new keeper supplement was stamped in their name as they taxed the car for me.

So, any ideas on how to proceed?