As miner says there are ways to do this properly, and the way proposed does not sound to be one of them. The facts can make all the difference, but the approach is fundamentally incorrect.
If the executor gets it wrong, and the payment is later challenged, he or she may find it necessary to stump up himself, and then to recover what he can from the carer. The question in law is 'who can give a good receipt?'
Miner has a particular view of the Court of Protection, which certainly has had its difficulties in the past, but if that is what is needed, there you must go.