Im aware Ken as flown to and from Japan with iaito swords, i can only presume these are not worth say $10,000 and up and are described as sporting equipment in the paperwork.
Purely speculation, but im hazarding a guess at some pit falls. Lets say you go to democratic country, the Chicago show and buy a sword from Joe the dealer at $10,000, he gives you the documentation in Japanese, plus a signed piece of paper saying its an antique. Your misses, to add a bit of humour is accompanying you on this trip of a lifetime (no ways shes missing this one). As always these kind of trips get of to a rocky start when you ask her why she needed to bring 15 pair of shoes for a weeks vacation.
We arrive at Chicago airport, go the the check in desk. i tell an inexperienced girl on the desk i have a nihonto sword in my suitcase, she says "i beg your pardon", i say, "an antique Samurai SWORD", she says "you cant take that on the plane". After a lot of time holding up a large que quibbling, she calls for a customs officer.
By this time your misses is not happy. Your led off to a room to sort things out. The main man who deals with this kind of thing is out, he arrives an hour later. He as a look over the papers, then says he needs to speak to the guy you bought it from. He calls Joe, but he is out partying with his sale money. It can go two ways, he can let you take the sword on board or not.
If not then you have obviously missed your flight, if he does, by then you may have missed your flight anyway. You get the next available flight via Amsterdam (at extra cost), an added worry of baggage going missing, but the grief your misses is giving you makes that worry seem insignificant. Your wishing you just got it posted.
There are other pit falls, but time is short.
If you think none of this is possible, your deluded.