I am a supervisor at a UPS in Ohio. The laws may be different where you live, but we ship handguns all the time. Here they must be NDA insured. Don't lie to them, we open all packages to check the contents. Wouldn't want to ship any bombs you know.
The few times I shipped, I would only ship the gun in two packages as parts and label them that way.
The easiest way to find out your local regulations is to ask a sales Rep. They should be scurrying in and out of the building all day, tell them you have a problem with an account, they will help you then.
What do I do when I need to ship a whole gun? I use Fed Ex. UPS is so anti-gun I won't give them the business in this respect, if my guns are not good enough for them, neither is my money. The new rules had little to do with security, it was all PC.
You should have absolutely no problem shipping to an FFL holder by NDA. Remember though, you must pay the extra $15 fee that they imposed on all of those evil handguns.
Fed Ex also imposed a fee on shipping handguns as well but it was less.