If you ship Fed-Ex you have to take it to their local hub. You tell them it's a firearm. You ship it overnight. They put your box in a special bag which gets an additional level of tracking and scrutiny. It's not a big deal other than the cost. They will not accept firearms at their stores for the same reason the USPS won't accept them. They don't trust their employees. If they don't trust them why would you? You can tell them it's parts at the store and they'll take it but you don't have to be a genius to see that the box is handgun sized and it's going to Taurus. Even a FedEx/Kinko's employee can figure out that it's probably a gun inside and that maybe that's one box that should disappear.
My suggestion is to take the gun back to the store where you purchased it, or your favorite local gun shop, and have them ship it. My understanding is they can ship USPS for about $10. Even if they charge you a $30 fee you are still only spending what you would with FedEx and that money is going to your local gun shop instead of FedEx. If I had purchased it at the store I would not have a problem paying the shipping cost through them but I would not expect any additional fees. If I didn't buy it there I would expect to pay both shipping and a fee for their time to do the required paperwork for them to take possession of it from you.
No matter how you slice it the process is a PITA thanks to dishonest USPS, Fed-Ex, and UPS employees.
I will only buy from companies that will send a return shipping label if the gun has to go back for work. At ~$40 each time a firearm has to go back it adds up quick if I have to pay.