There were plenty of exotic weapons in Japan, and also more than just a few in China. Leaving aside questions such as "Is there such a thing as a ninja weapon?", "Were ninjas real?", etc., we can still ask who used these weapons, and why.
First, we can note that exotic weapons were not common weapons - otherwise, they wouldn't be exotic. Battlefields were dominated by gun, bow and crossbow, sling, spear and other polearms, and the sword. Perhaps the most common exotic weapon on the battlefield was the war fan:
which was used by commanders to signal to their troops. Since they would be holding it in their hand during the battle, they were often (like the linked example) made strong enough to use as a parrying weapon, and sometimes strong and heavy enough to use as an effective club/mace.
The war fan could be a weapon disguised as a fan - a member of a large group of exotic weapons, namely disguised weapons. Disguised weapons were typically made to look like a more innocent object. Examples include iron flutes, tobacco pipe clubs, other types of iron fans (tessen), sword-canes, knives disguised as folding fans, staves with hidden spear blades, and staves with a hidden ball-on-a-chain.
There were also hidden weapons, made to be easily hidden in one's clothes, but not disguised. There were, necessarily, smaller than the larger disguised weapons. Examples include small knives, shuriken, various knuckle-duster-like weapons, and some chain weapons (e.g., the manrikigusari, a short chain with weights on the ends, could be hidden).
Disguised and hidden weapons were sometimes carried by people who were not expected to be armed (e.g., a monk might carry a staff with a hidden weapon), and by people who wanted to be armed in places where weapons were not allowed, and by people who wanted to attack an enemy by surprise. Weapons like these might be attractive to criminals, but were used by other people, too. There would be little point in using disguised/hidden weapons to try to appear unarmed on a battlefield.
There were also special-purpose weapons. Some were designed to give a better chance against some opposing weapon (e.g., a spear or sword) while being easy to carry. For example, a kusarigama (ball-chain-sickle) offered excellent range, and gave the user more reach than spear or sword (but there might be serious problems if they missed their first attack against a spearman or swordsman attempting to close). Chinese double-swords gave an improved chance against a spearman, while being only a little more difficult to carry than a single sword (and much easier to carry than a spear or shield). Weapons like the Chinese hook sword gave excellent prospects of trapping an opponent's weapon with the hook (especially when used in pairs). Other weapons might simply have tried to take advantage of an opponent's unfamiliarity with exotic weapons. These were not weapons for everyone - they were weapons for those with the time to train with such exotica, and the expectation (whether realistic or paranoid) that they might need to face a spearman or swordsman. The smaller weapons like these, while not necessarily designed to be hidden, could be hidden much more easily than a full-length sword or spear. Such weapons appear to been mostly used by criminals and bodyguards, and also by martial artists in street performances.
Probably the most widely-used special-purpose weapons were police weapons, typically less-than-lethal weapons intended to make it easier to capture a criminal alive than if using gun, sword, or spear. Police weapons included the jitte/jutte, naeshi, manrikigusari, and specialised man-catcher polearms (in Japan), the sai and tonfa (in Okinawa), and the iron ruler and sai (AKA cha) in China. Various wooden and metal truncheons and staves were also used as police weapons. Modern police forces (and other security workers) still use many similar weapons, such as truncheons (and in some places, staves), and man-catcher polearms:
(In addition to old-style exotic police weapons, some new types have been developed: https://www.youtube.com/watch?v=k5Mgc84iLvU.)
In summary, exotic weapons were rare on the battlefield. In particular circumstances, they could give an advantage, or at least reduce the disadvantage against a well-armed opponent. Some specialised weapons were difficult to use, and needed a lot of training. Other specialised weapons would be inferior on the battlefield, but saw use due to that inferiority (as less-than-lethal police weapons).
If you can find a copy, Serge Mol, Classical Weaponry of Japan, Kodansha, 2003, provides an excellent survey of Japanese exotic weaponry.