I just went round & round with the same thing since I needed to ship 3 handguns to an out of state dealer. ALL the dealers I talked to (3) either would no way do it or insisted on UPS next day air....$$$$$$$$$$$.
Well, What I found out is it definitely has to go 01 FFL dealer to dealer (C&R FFL not acceptable) but you can in fact ship handguns via USPS as long as you have the dealer fill out a PS form 1508 and give it to the PO clerk to file. I happen to send the handguns Express Mail that was about $80 cheaper than UPS. When I was with the PO clerk doing this, I asked if they could ship these hand guns via Priority Mail and she said they can but they "prefer" sending handguns Express. The problem comes in trying to tell a dealer what I just told you. They are fixed in their ways and here I am with my hat in my hand..... I had to grease the wheels a bit heavy to git her done!