You are notably missing Greece, which Pankration is
probably the basis of *all* martial arts (born by Spartan warriors and learned by Makedonyan oplytes, then expanded to all Asia with Alexander, to forge there the basis of Easter Martial arts in India which from there were brought -with of course enormous differences- to China... just a common theory anyway)
Your question is interesting but I'm not getting if you're referring to simulate the diifferences through Dom3-mechanics or another random game...
About the specific styles - in Europe we got mostly
warriors practicing martial arts: practice war-arts, put some focus on your favourite weapon but you must be an all-around fighter, no time for style in war. Exception: Theutonics, Templars which were also warrior monks.
Asia: warrior monks practicing martial arts as a way to achieve perfection for body and mind. Highly acrobatic and coordinated styles. Different weapons coming from several needs (all those weapons coming from the law that paesants couldn't bring swords so you have to conceal self-defense weapons as agricolture tools
).