I ship all rifles and shotguns by US Postal Service registered mail. They go priority mail and can be insured for up to $50,000. The postal agents may not ask what is in the box, but some do.... Nuisance is that registered mail uses the special paper tape that has fiber in it and uses water to activate the glue on it. Staples carries that tape, also called Kraft tape. Believe you'll find the Post Office cheaper than FedEx.
Good advice above on including self and buyer details inside the packing. If the gun has a case, go ahead and put peanuts inside to minimize barrels or stock moving around during shipment. I have a nearby UPS packing service that then puts the gun case in a stout cardboard box.
Regards
