On a side note, you are not required by law to have the handgun shipped overnight. Our local store/distributor charges $18 and ships everything ground UPS.
That needs a clarifier. An FFL holder can ship a handgun through USPS priority mail and it will arrive in 3 days or less. A private citizen without an FFL cannot do this through the postal service and has to ship overnight with a private carrier. The private carriers, UPS and FedEx, require overnight delivery for a handgun to the best of my knowledge. The key to all this is if you have an FFL. Now an unscrupulous person might decide not to tell the private carrier what is in the box, but I'm not touching that with a 10 foot pole. This is all just my understanding.