Depending on what he said in the dispute, mail a small package to his address and pay for a tracking number. Provide that to PayPal.
What you're basically suggesting is: scam PayPal because OP was dumb enough to sell Bitcoin using a reversible payment method.
Besides it wouldn't work anyway. It's an "unauthorized" claim and if OP ships a package AFTER the claim was filed it won't qualify for Seller Protection even if it otherwise would.
I'd say at $39 it's not a very expensive lesson to learn.
It's not scamming PayPal, it's protecting the seller who did nothing wrong. And that method has been proven to work. The dispute will be closed once the package has been marked shipped and then PayPal will do a small investigation on the tracking number, as long as it exists and is being sent to the correct address he has nothing to worry about.