I don't think you can ship a handgun to FFL without using an FFL. My LGS says they got a handgun in from someone without FFL, and they wont transfer it because it came from non FFL. I do not know~.
It is legal, however it is up to the receiving FFL as to whether or not he will accept it. Even though it is legal, a non-FFL cannot ship a handgun for the purpose of selling the handgun, through USPS...so it would have to be shipped using a common carrier such as UPS.