Proof of postage does not count here, it's proof of delivery which matters. You do not have to use Packlink, I never did when selling.
Only tracking showing delivery will close any case a buyer opens for item not received, and then you would not have to refund.
Use those proof of postages now, to claim compensation for yourself from Royal Mail, or from the courier you used, for a lost item.
If it was RM , you need to wait 15 days before you can claim compensation.
@paul_w92