The legal requirements for shipping hazardous materials are complex and involve a lot of things depending on the specific classification of the materials, that the general public is unaware of. Things such as physical position of the materials in the truck, relative to other things in the truck, for just one.
Proper placarding of the truck is another, the list is long, and involves both chemical safety regulations and worker right to know laws as well.
The proper, legal CYA method is to inform the shipping company, let them meet all the needed regulations and pay their price for doing so.
Most people would simply put it in a container and not tell the company so as to save a few bucks. This is the "everything's legal until you get caught" school of thought, and we advise NOT doing it.
Consider, for a moment, the possible worst case situation. You "sneak" your ammo into the shipment, and something happens where the shipment is involved in a traffic accident, or some other thing where it is discovered, and its NOT on the shipping manifest.
Now, not only have you caused the shipping company to violate various regulations and/or laws, but you lied to them, in order to do it.
Neither the government, nor the shipping company will look kindly on this, and some fairly serious fines (or possibly worse) could result, and almost certainly cost you FAR more than the extra charges you would pay having it declared and shipped in compliance with the law.
Also, there is the possibility of violating your contract with the shipping company and their insurance carrier, which could cause further issues.
It is within the realm of possibility that if you are found in violation of your contract, any damage claim for any of the rest of your shipment (including the car) MIGHT be disallowed.
Do the right thing, and pony up the cash to cover all the charges. If nothing bad happens, write it off as money "wasted". BUT, if something bad does happen, you'll be very glad of every penny you spent covering your butt.
Me, I'd put it in container(s) that meet the most restrictive state requirement of those states I'd be driving through, and go for it. I'd also be willing to drive more hours and miles to avoid NYC and NJ, but that's just me.
Good Luck.