I'm not a lawyer, but were I you. I'd have a bill of sale for the transaction with the buyer's name and other personal information.
Should the gun be traced back to you, you have proof of the private transfer.
NRA Chief Range Safety Officer, Home Firearms Safety, Pistol and Rifle Instructor
"There are three classes of people: those who see, those who see when they are shown, those who do not see."
Leonardo da Vinci