UPS allows shipping via different next day air services:
Handguns, as defined by 18 U.S.C. § 921, will be accepted for transportation only via UPS Next Day Air Services, specifically, UPS Next Day Air® Early A.M.®, UPS Next Day Air®, and UPS Next Day Air Saver®. (Note: UPS Express CriticalSM Service is not available for firearms).
I think the Air Saver is the least expensive (note that didn't say "cheapest").
Jim's Rules of Carry: 1. Any gun is better than no gun. 2. A gun that is reliable is better than a gun that is not. 3. A hole in the right place is better than a hole in the wrong place. 4. A bigger hole is a better hole.
no guns = might makes right