UPS is fine with muzzleloaders going to an individual, but God help you if they get damaged, as it's a long drawn out process to get a claim paid. UPS is the hardest on packages of any carrier.
USPS is fine to ship to an individual also, and very safe and reliable. They would be my first choice.
FEDEX is also fine, and very good handling packages. SOMETIMES, they will not take them no matter what they are at their hubs, BUT you then have two choices. One, get a manager and explain the muzzleloader regs, OR they will pick it up at your house, if you have a FEDEX account, all you have to do is create one. FEDEX is cheaper, and as I said, good at package handling, they are my second choice.
Some FEDEX hubs have changed over to only overnight shipping centers, is my understanding, that they will take them, but they would have to go overnite and the last time I looked that was over $150!!
The short simple answer is, that with MAYBE, the single exception, of the Ruger Old Army, no muzzleloader is governed by any Federal laws. Thus no serial # requirements.
Now, as an aside, there is some brewhaha over the ROA because of the availability of after market .45 Colt cylinders, thus making it a cartridge revolver. My take is, that as of now, if you don't have a .45C cylinder, and certainly aren't shipping one with a ROA, then all is fine. I bought one for Christmas, and it was shipped right to me. Personally, I think if you want a .45C, buy one, leave the ROA a BP gun. Only my opinion.