The firearm must be shipped to an FFL, not directly to the buyer.
From the ATF website:
(B7) May a nonlicensee ship a firearm through the U.S. Postal Service?FedEx will ship handguns.
A nonlicensee may not transfer a firearm to a non-licensed resident of another State. A nonlicensee may mail a shotgun or rifle to a resident of his or her own State or to a licensee (FFL) in any State. The Postal Service recommends that long guns be sent by registered mail and that no marking of any kind which would indicate the nature of the contents be placed on the outside of any parcel containing firearms. Handguns are not mailable. A common or contract carrier must be used to ship a handgun.
May I suggest a firm return policy. Five days, two weeks...
If never fired, will the firearm be allowed to be fired and still be accepted for return?
Postal money order?
Also, something to think about before you decide to not follow federal law, let alone your own state laws and just pop it in the mail.
If the firearm is used in a crime, suicide or whatever, what is your liability if a lawsuit is brought by an injured party who finds that you did not follow the law?
(B5) Are there certain persons who cannot legally receive or possess firearms and/or ammunition?
Yes, a person who –
(1) Has been convicted in any court of a crime punishable by imprisonment for a term exceeding 1 year;
(2) Is a fugitive from justice;
(3) Is an unlawful user of or addicted to any controlled substance;
(4) Has been adjudicated as a mental defective or has been committed to a mental institution;
(5) Is an alien illegally or unlawfully in the United States or an alien admitted to the United States under a nonimmigrant visa;
(6) Has been discharged from the Armed Forces under dishonorable conditions;
(7) Having been a citizen of the United States, has renounced his or her citizenship;
(8) Is subject to a court order that restrains the person from harassing, stalking, or threatening an intimate partner or child of such intimate partner; or
(9) Has been convicted of a misdemeanor crime of domestic violence
(10) Cannot lawfully receive, possess, ship, or transport a firearm.
A person who is under indictment or information for a crime punishable by imprisonment for a term exceeding 1 year cannot lawfully receive a firearm.
Such person may continue to lawfully possess firearms obtained prior to the indictment or information.
[18 U.S.C. 922(g) and (n), 27 CFR 478.32]