I would send it Special Delivery (unless the seller has an issue with signing for a package).
No need for a return address (as you'll give the seller your bitcoin address through the net).
Then you'll know for sure if the cash has arrived, and you'll stay anonymous, unless I'm missing something...
No return address is not a good idea because if the letter cannot be delivered for some reason, the post office will open it. And your money will be gone forever. It is best to use a private mailing address.