This is what I would do.
I would take the item to the Post Office and simply pay for postage to get the item sent and keep the buyer happy.
Add the tracking to Ebay - if you can't do this, contact Ebay Customer Services and ask them to add or change the tracking.
Let the buyer know that you have had an issue. Tell them what service you have used and share the tracking number with them.
Cancel the label bought through packlink.
"There are two ways to be fooled. One is to believe what isn't true; the other is to refuse to believe what is true.”
Søren Kierkegaard, Danish philosopher (1813 - 1855)