Dunno about shipping handguns via the USPS, but Beerslurpy's right about carrying. IANAL, but it appears that if you've got a "permit",
and your state doesn't include a prohibition (like OH does!), you're OK.
AFAIK, the USPS doesn't accept handguns at all, although others on this thread have indicated that FFL's can use it. There would be no problem shipping "parts", but the ATF considers the frame (actually, the part with the serial number) to be a handgun, so you could ship a barrel, or a slide, or a cylinder, but.... Splitting it up into two packages might be a problem. I'll wait for wiser heads
....
Here in OH, our "anti" friends didn't read the Federal regs completely. They really don't want anybody to carry, so it's one more hurdle.
The former day job was a plastics company. We needed to ship some effluent water (the stuff that hits the drains after being used to cool the product during manufacture) to a laboratory for analysis. Five gallon jugs of not-quite-Haz-Mat material.... Not a peep from the PO.... But you should have been there the day that I tried to mail some plasticizer samples....
("Plasticizer" is an organic chemical - there actually are a bunch of them, and I can't even remember which one this was; it was over fifteen years ago - that's used to make vinyls flexible. Usually clear to light amber in color, but it handles like Hoppe's oil when you try to clean it up, etc. About as flammable, too. That's what got 'em excited. "It'll burn?!" Actually, it will, but the flash point is high enough you can crush out a cigarette in it without risk. Just makes a mess if you spill it....)
They took the stuff, but it took us a half-hour with their book to figure out what to call it, and whether to accept it.
Regards,