Mr. Smudge, I've flown all over the world, including 6 trips to Africa, and have never taken ammo in anything but a standard plastic case. That meets any airline stipulations I have ever seen. I print out a "label" that lists me as the manufacturer along with number and cartridge designation, but that is NOT necessary, just looks good. As mentioned by Mr. Scrofa, I put in a piece of styrofoam or foam rubber to prevent rattling, also I tape the box shut. I use electrical tape, and if you are a bit careful when you're there, you can salvage the tape to re-use on your return. But I always have some electrical tape in my plunder anyway. Comes in handy. That is for reloads, which is all I ever use, but if you are taking factory ammo, the original box is all you need. Note that you are almost universally limited to 5 KG (11 lbs) TOTAL of ammo, but that is way more than you will need unless you are taking a shotgun (which you haven't mentioned). If you take 30 rounds, unless you are a horrible shot, you will return home with about 20 of them! I never take more than 30, usually only 20. Ammo goes in your checked bag, NOT your gun case, and you should declare it at check in. Just say "there is ammunition in my bag". No surprise to them, because you are checking a firearm. The Tuffpac you refer to is an expensive solution to a problem that doesn't exist. Save your money!
Do you have laminated tags with your name and address on them (and ties) for each of your horns and capes? A good idea to do, though not a requirement. Helps assure you get your stuff.