Yes, there had to be a European origin to this pistol style. It seems like it never caught on in Europe. But as mentioned, it was certainly popular in the Eastern markets for a long time. Another one of these Eastern mysteries.
Yes, knee pistol is a curious analogy. But notice some of these pistols (unlike Corrado's) have an even more curved butt plate. I took one of these with the extra curve and sat on a chair and positioned it over my knee. It does fit very well. LOL Although I would not want to try firing it off my knee without a leather pad. LOL And maybe this is what they did (?) With a pistol size load and a leather pad, I could see this doable. I'm somewhat more inclined to think the butt was pressed against the saddle or waist/hip. There does not seem to be any real historic evidence one way or the other.
One thing I have noticed on all these knee pistols is the wide/thick grip area. Obviously for added strength.
Come to think of it, at our shooting range there is a cowboy action area with a manican horse. Maybe I should try this out ? LOL