That is how I would do it.
In fact, when I sold my camper afew years ago, it was two days before the end of the month and I said to the buyers if they liked I would declare transfer of keeper right on the last day so they didn't have to buy a full month tax for just 1 day of use. Or they just don't use the vehicle on the final day? whatever they liked.
Whilst a road camera could possibly pick up an officially untaxed vehicle due to change of registration, no one is going to chase up 1 untaxed day for an unused vehicle surely? Given you can post these forms rather than do it on-line, there has to be a few days of grace minimum for postal times?
(my own issue was that for some reason I couldn't tax my new van in my own name as it was already taxed in the old owners name despite me having the V5 in my name. very odd and not how it was meant to work (tax is meant to automatically get cancelled). And I had to SORN it in order to cancel the tax and start again. On the plus side, it was ME who got 10 months of tax refund, not the original owner
)
Note if someone concerned they would pay over money and not have ownership until a couple of days later .... ownership of a vehicle and being the keeper are different, so they still get a receipt showing they now own it, and get the V5 slip. It is a matter of trust I guess and you would hope a buyer/seller relationship would be trusting enough?