Right now your ability in any given martial art is determined by your melee and unarmed skill. Once you’ve mastered one, you’ve effectively mastered them all, provided you find dojos and spend a few minutes reading up on the new styles.
Martial arts should be like the various gun categories. There’s a generic gun skill, and an individual skill for each class of gun in the game. Perhaps “Melee” is considered the generic type, and there’s a different skill for each martial art type. Untrained characters fighting bare-handed can start with a “street brawler” fighting style, or something else that implies an improvised style.