Ok, the closest thing I could think of to these knives (as far as Crap What Done Comes Outta Japan) is the small dagger that anime/samurai movies give to literally every woman in existence, and is almost always immediately knocked from their hands (because they are women, women can't STAB things, that's obviously a man's job, because manliness is all about thrusting)
that's a cultural idea based on kaiken, short knives carried by samurai class for slashing up folk when you need folk slashed up, but you don't have a sword because you are inside, or are a woman and logically incapable of carrying a sword because come on, that's just silly.
As far as I can tell, though, there isn't a "rule" that establishes the shape of the blade as "kaiken", but rather that the word refers to a short dagger/tanto that specifically is not part of your "two swords" stuff.
Also a fun note: if the knife actually is used to kill someone in fiction, it will usually be the owner, because seppuku.
but yeah, my knowledge base on all the nuances of japan's weaponcraft is very limited, I really only ever studied the culture and history.
