What boxes? There is no "box" at fedex.com to check to indicate you are shipping a handgun, much less any other firearm.
Well, first that link IS NOT FedEx, but a third party who isn't close to accurate.
If you want to read FedEx's tariff straight from the horses mouth go here:
https://www.fedex.com/en-us/service-guide/terms/express-ground-samedaycity.html
Click on "FedEx Express U.S. Terms & Conditions", then scroll to "Firearms"..................you then discover that
ALL FIREARMS shipped via FedEx Express require Priority Overnight.
But wait, it gets better.....
If you click on "FedEx Ground Tariff", then scroll to "Firearms" you'll discover this nugget:
So, again, shipping a handgun via FedEx requires Priority Overnight. This isn't anything new, having been FedEx policy for at least fifteen years.