Hi, omorik. Welcome to NMB.
I've been lurking for a while, so this is my first post as well.
Firstly, I'll direct our attention to the lovely Search feature availiable at NMB, SFI, myArmoury, etc. Trite, yes, but useful since it's certainly not the first time these "problems" have occured. So I found this thread:
http://forums.swordforum.com/showthread.php?t=65959
There's another two threads I think I've seen, but can't find them off the top of my head. AND, from my personal experience, I would not use a triangular cardboard shipping box, they will not roll off the ground but they are very flimsy.
The best method that I would use for sending a bare blade through the mail, if kodogu/shirasaya was NOT availiable, would be to first wrap it with soft cloth or paper to prevent surface damage, then sandwich it between two pieces of heavy cardboard and close the cardboard tightly around the blade, like you would use your hands to stop a blade in a chanbara movie. Review how a sword cuts to see the objective here: to cut with the edge, there is contact with the edge, pressure and usually movement. You want to keep it from moving around.
It's also possible to use wood, plastic and other materials to achieve this effect, + additional protection for the kissaki is also a good idea.
I just take two heavy pieces of cardboard, trace an outline of the blade on both sides of the cardboard, then use screwdriver or a punch to create some hole openings. Cut out appropriately, lay the sword inside and then close cardboard sheets around the blade using the holes using zip ties. Send one through the mekugi-ana for good measure. If you have plastic male-female fasteners, that's fine too but I would stay away from metal screw fasteners or metal of any kind just in case. The method of is up to you, but be very careful if you are going to use a cardboard stapler, to avoid "stapling" the sword (!).
You should now have a friction fit "shirasaya", where the blade will not move around in there if it is shaken - preventing internal inertia movement. However, it will not protect from a broken tip or sides if it is dropped. Hence the energy absorbers. Take foam, cloth, soft whatever and ATTACH it to the outside of the cardboard using packing tape. Do not use shipping peanuts since they will shift around and the item will move around in the box.
Now, to make sure that everyone is safe when opening the item, you want to put a simple instruction on the inside of the box for how to remove it. If you use the zip ties to secure the cardboard to the blade, the zip ties should be cut and it'll come right out. Just my idea, I haven't much experience with using this since the only time I had to do this was once when I sent a dynasty forge blade for a tsuka recore and fittings. Everything did arrive okay.
This is a disposable package, so don't use this for anything international or the packaging will likely not be put together back at customs. For that I would probably try to hack up the closest thing to a "shirasaya" as you can make, PVC pipes if necessary since Customs is brutal with all items!