Ouch....
I think we were dancing around two maypoles at once here....
When we're dealing with a "will call", such as S&W uses, then the rules are somewhat different.
For an individual, the quoted Federal Law (or Regulation) is accurate, and FedEx OR UPS insist on "Next Day Air" type service (called by different names, probably). You must notify the carrier that it's a firearm, too. If you manage to get 'em to take a box of "machine parts" and ship it by one of their standard rates, you're likely cooked if there's some kind of inspection, or a loss - insurance or otherwise.
So you pay $80-ish and notify....
(You can't ship a handgun via USPS at all, although I think an FFL can.)
Now, if you're using a "will call", S&W or whoever is the shipper, and while the carrier is supposed to be notified, their rules (or at least their deal) with the carrier kick in, and notification is about all we're responsible for. If the driver accepts the package with S&W's name on it, then the notification is kinda moot, and should there be a problem with the shipment, you should be OK anyway.
Had a loony one about 2006.... The rules may have changed a bit since then. I printed up the necessary FedEx waybills and popped over to Kinko's with the package (handgun). The countergal at Kinko's refused to accept the package, even though FedEx's web site said that they would accept it. She must have had a similar issue at one time or other, 'cause she had a copy of a map page for me showing where the Terminal was, way the heck across town.
After politely telling her that I'd be cancelling my FedEx account, I headed out. Couldn't decide whether to go home and print up UPS paperwork (and cancel the FedEx bill), or just drive over to the Terminal. I decided that it was a nice day, and I could stop in at a Client's site while I was over there.
The supervisor at the Terminal agreed with me (and accepted the package) and apologized. I sent a nasty letter to FedEx, and got a polite response, too.
FWIW, I believe FedEx won't take those packages at what used to be Kinko's anymore. (It's not called that anymore.) And UPS' "UPS Store" locations won't, either. I believe that the local UPS Terminal (which will accept firearms) is a CPZ, though. The FedEx terminals might be by now, too. ("CPZ" - "Criminal Protection Zone" - no carry....)
I've given up - my pet local gun pusher now handles firearms transfers for me on the rare occasion that I need one. About $40 if I smile nicely.... I've never had a Will Call, though.
Regards,