FFL 03 cannot ship handguns via USPS.

PS Form 1508, used by regular dealers, requires the statutory declaration that the shipper is "a manufacturer of firearms or a bona fide dealer therein".

As 03 is a collector's license, not a business license, the collector is neither a manufacturer or a "bona fide dealer", and does not qualify for the PS 1508 handgun shipping exception.

I'll leave the dealer shipment part of your question for FFLs more local to you to answer, if they wish.