Whether an 03 can ship via USPS or not, its only going to apply to C&R guns as that is the ONLY firearms an 03 can legally transfer, without using an 01 dealer.
As for the original poster:
You have two options
1) use either UPS, FED EX, or some other common carrier. Take the packaged gun to the shipping counter, declare its a firearm ( be prepared to prove its going to an FFL ) cough real hard and hand em the monies.
2) Find a local dealer who will do the transfer on your behalf, pay the shipping and perhaps a transfer fee, smile hand over the cash and have a nice day.
Adding in a transfer fee, the options will likely be very close in price.
When the buyer sends his monies, have him include a copy of the receiving dealers FFL, you will most likely need it, if not for yourself, then for the dealer who does the transfer for you.