5 years ago I used UPS to ship a handgun to myself. I shipped it from CO to Alaska. I was required to ship over night. The ATF website had some good info on this and specifically showed that this was legal. I printed out the ATF stuff and the UPS policy pages and took it with me when I went to the UPS facility to ship. I did have to show this info to the UPS person before they agreed to help me!

From your description, I believe this is allowed, but that was my experience 5 years ago. Check the ATF site and be prepared to help "educate" the UPS or FedEx workers.