Federal law says no private HANDGUN shipping using usps. So no chance.
Fedex and UPS has a rule that says if you don't "declare" as a weapon, they will not guarantee the shipment. $75 to $80. This is a rule, not a law.
I almost never get asked what's in the package and when I do I say "parts". I don't think these shippers would pay anyway if the package was lost. Forget the warranty. Pay $10 - $20.
When I've sold long guns, I ship myself which ever way is cheaper.
when I've sold handguns, I take it to a local FFL and have them ship it since they can ship it through 'regular' ground shipping, ie way cheaper. I box it up, pay them a bit for their time, and they take care of the rest.