You can ship a rifle through the USPS, FedEX or UPS back to the manufacture for repair and to a gunsmith for repair/work without using a dealer. I have used UPS and FedEx a few times doing this. If shipping with UPS you must go through a UPS hub and not a privately owned UPS store.
Now with a handgun, it must be sent nextday/overnight. Long guns can be shipped ground.
I have to stress that you need to make sure the packaging needs to be very secure. I dont know what the carriers do but there is some rough handling for sure. I sent a Cooper back for re-stocking and went it arrived in Montana, the barrel was protruding out of the box and I had shipped in a double box as it came from Cooper. Cooper was kind enough to recrown the barrel at no charge.
I sent all the parts for a build to my gunsmith in the midwest in a padded dockosil guncase that then went into a cardboard box a few months ago, when it arrived I was notified that the fluted barrel was somewhat damaged. The smith had to file/stone out gouges and nicks from the bbl. I am getting that completed rifle back in a few days and hopefully it will come back undamaged.
Not trying to scare you but this is something to think about.
Have the manufacturer send you a copy of their FFL license. Print it out and have it with you when you go to UPS.
I have done this in the past when selling and shipping fireams to a FFL but have never been asked for it by a shipper.