As always, my advice is based on what I would do.

You have messaged the buyer and told them to keep the record - you think it's unlikely they will respond to your message.

For me, the simplest way to  sort this (as you seem prepared to take the loss) is just to send the correct record out to them.

You could send one further message (but don't repeatedly message them) saying it's on its way and giving them a tracking number.

This will be a financial loss to you, but you should have a satisfied buyer.