Nope, shipping hazmat material requires special certification training,computer generated hazmat labels, the right type of shipping boxes plus a few other things if I remember right. (I'm a ups driver).
That is BS, if you are talking about a UPS shipping center they do not know the law and are trying to cover their ***.
The "UPS Stores" are franchised and not usually owned by UPS, these guys will not except firearms because they don't want the liability.
Fairchase - certain types of cardboard boxes are not allowed to ship hazardous materials in. While an approved box may seem like a "normal" box there are certain requirements and not all cardboard boxes meet those requirements.
The UPS requirements are the same anywhere you go. You might get away with it if you don't tell them what you are shipping and do not label the box but it is certainly not worth the risk to me. Fines are in the 1,000's of dollars
While it may seem like it is just a simple sticker on the box, it takes quite a bit of money ($250 just to take the test) time, training, etc to become an approved hazardous shipper in order to get those stickers.
Do some searching on Google about this, or even better yet go to the UPS or FedX web site and read about shipping hazardous materials.