In reference to shipping firearms by USPS or UPS, it depends on who is on duty at the particular location you wish to ship from. Some clerks either do not know the rules or possibly do not wish to facilitate the transfer of firearms. (I lean to the former explanation, based on experience with "customer service" at other places.) I recently had to visit three different post offices before I found a clerk who knew that individuals could ship long guns to FFL holders in another state. I was using the USPS because the clerk at the local UPS office wanted to charge me next-day rates for a long gun when the rule requiring that rate only applied to handguns.
You may be able to get a UPS or a USPS employee to consult the written policies and procedures and follow them, but you probably won't make any friends that way. Just be advised that when trying to ship a firearm the person you are dealing with may not know the rules and be prepared for the possibility. I have no direct experience but i suspect the same caution may well apply to FedEx. Note that UPS polices are available on their web site, and the USPS Domestic Mail Manual is available online. It might be a useful tactic to print out the relevant portions and take them with you when trying to ship a gun if you aren't familiar with the people you will have to deal with.