If you were to change the vehicle class status yourself you would need to fill in form V70 and send it to the DVLA along with the V5C(log book) and a copy of your certificate of entitlement. You would then get a refund withing 6 weeks on the remaining full months VED. From memory I don’t think you can change the class status at a post office.
However it cuts out the faf if you get the dealership do it on the day you hand your mobility car back and collect your new vehicle.