Not an entirely straightforward question, Mark. First the easy bit, from the Club's perspective, once you sell the vehicle, please make sure you remove it from the club records by logging on to your profile on the web site and go to edit profile and remove the car.
Now the tricky bit - doesn't matter if it a C4C or a 404 concession, most of the work will have to be done by the purchaser, but the status of the license may determine how much they are willing to pay for your car. If they are a club member (us or another DoT approved club) then its easier - the purchaser gets a signed CMC 1 form (404) or E116 (C4C) from their club and takes that along to licensing when they transfer the vehicle. Easy.
Without that paperwork the vehicle will have to go back onto full reg at that time. And this is where it can get messy. If there is not a DoT record that the vehicle was ever on full reg (unlikley but possible if it was originally a ground up restoration or build) they may want it inspected first, but even if it was, a 404 vehicle will now be subject to stamp duty as it is transferred. C4C wears stamp duty always. Arguably, all of this is the purchaser's problem but they need to go into it with eyes open or it will just cause agro. Cheers Andy