From the UPS service guide:
Special Procedures for Shipping Firearms
UPS accepts packages containing firearms (as defined by Title 18, Chapter 44, and Title 26, Chapter 53 of the United States Code) for transportation only (a) between licensed importers, licensed manufacturers, licensed dealers, and licensed collectors (as defined in Title 18, Chapter 44 of the United States Code), and government agencies and (b) where not otherwise prohibited by federal, state or local law (i) from an individual to a licensed importer, licensed manufacturer, licensed dealer, or licensed collector; and (ii) from a licensed importer, licensed manufacturer, licensed dealer, or licensed collector to an individual.

The shipper must comply with and must ensure that each shipment containing firearms complies with all federal, state and local laws applicable to the shipper, recipient, and package, including, without limitation, age restrictions.
If you address the package as per the BATF FAQ to yourself in care of some one else that has to be an FFL. Most UPS offices (you cannot tender firearms to franchises like The UPS Store) the counter people will ask to see an FFL (see paragraph (b) above) and check the address on the package to match.
Deflave, I am not being argumentative. If your local UPS is still allowing you to ship without involving at least 1 FFL holder in the transaction, they won't be doing it for long. Again from the UPS service guide:
Getting Your Firearm Shipment to UPS
Firearms (including handguns) may be shipped only through a UPS Scheduled Pickup Account (specifically, Daily Pickup, Daily On-Route Pickup, UPS Smart Pickup®, and Day-Specific Pickup), or through a UPS Customer Center (counters at UPS operational facilities). Note: Firearms (including handguns) are not accepted for shipment via UPS Drop Boxes or UPS On-Call Pickup®, and may not be tendered to or dropped off at locations of The UPS Store®, any third party retailer, or any UPS Access Point™ location.

When you are shipping a package that contains a handgun, you must verbally notify the UPS driver or UPS Customer Center clerk.