The big two-handed falchions were Saracen, i.e. modern Syria. They were not nearly as common as fiction portrays them, since the Saracens valued their archers, and particularly horse archers, over shock infantry anyway.
The Persians of the period were part of several different nationalities, all loosely grouped with the Saracens and the Arabs under the banner of an Islamic world empire. They did all share similar weapon designs and weapon-production techniques, including composite-construction recurve bows and the original narrow straight-blade "seif" (as in "Seif al Islam" - the sword of Islam, the symbol of Jihad). However, being more of a desert people, the Persians had always been much more horse-intensive (infantry is pretty useless in the middle of a huge dry flat area) ... so they tended to gravitate more to sabers and spears than to two-handed swords.
That, of course, being completely irrelevant.
Reality is that the province of Iga did train troops in covert operations, and everybody knew it. One emperor (I would have to look up which one) referred to the shogun's spymaster as "A Bushi of far-away Iga Province." Part of the reason was just adaptation to the environment, since the province was out in the hills and kind-of off the beaten path ... better terrain for a guerrilla war than trying to force a pitched battle. The other reason was supply and demand - everybody needed special-forces troops, so Iga trained them.
The "ninja" (roughly translated "covert operations troops") and "shinobi" ("spies") were in high demand because political intrigue was the order of business. Therefore the Japanese got very good at it. Much of the technique used by modern spies, snipers, and other covert operatives is derived very directly from the old Japanese forms. Like their modern counterparts, the ninja of ancient Japan were professionals at what they did ... they were cold-blooded killers. Some had good reasons (like getting rid of very bad people before anyone else dies), some worked for whoever and didn't care who they killed, kidnapped, or otherwise harmed. They worked in espionage, and in counter-espionage, terrorism and counter-terrorism, sometimes all at the same time. They were alternatively named heroes for their courage and skill, or marked as cowardly back-stabbing thugs ... just like how modern snipers are treated. Some were samurai ... some were peasant-born. One thing, however, can be said for all of them ... like their modern counterparts, they were very good at what they did, and no matter if you loved them or hated them, you had to fear them. They were dangerous people.
The Hollywood "ninja" is part of the post-WW2 "martial arts" craze, and like most of its contents, retains some of the appearance of the original without understanding its content. This is where the idea falls apart - trying to make the most absurd stunts look like standard procedure. I mean, climbing a 30-foot wall and sneaking into a military base at night is generally a poor way to set up a hit, unless you're on a short time table and just don't have a choice. Catching the fool out shopping, when he only has a couple of goons with him, and putting a knife in his back is much more efficient. A bullet or crossbow bolt from a second-floor balcony is even cleaner. Or poison in the water supply (although that will likely have heavy collateral damage, in the form of whoever else drinks it... that could work for or against you). But those moves wouldn't make for much of a movie, because the stunts would all look like the kind of thing that middle-aged slightly-overweight guys could do. So they go for the most extreme examples, to show how cool they were ... when, realistically, extreme tactics usually mean that the more practical plans have failed. Granted, the practical plans do sometimes fail, and people try the most absurd stunts out of desperation ... but in reality those stunts weren't because they were cool ... it was because they were running out of options.
And this is the base line of covert operatives in any time period. The same can be said of fiction involving modern or semi-modern special forces teams.