UPS will ship ammo, powder and primers. Or at least they did in the past. You just need to have that placard taped to the side of the box and pay the added cost.
Not according to the UPS web page. UPS Stores won't accept anything firearm related, but since they aren't an actual UPS store, then it's just their policy. Take your ammo with the Hazmat placard to a UPS depot and they will accept the ammo.
There is no list of approved Hazmat shippers that ship for the general public. One can't just walk into a business that you know is Hazmat certified and ask them to ship a PKG.
I mean you could
I don't think it will work.
Your only real work around would be if you had a friend that was a certified Hazmat shipper. He could then ship it for you, if he wanted.
Unfortunately, the general public can't ship Hazmat Pkgs with UPS or FedEx.