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.
Then don’t put them in the normal skill display. They can be treated differently than normal skills. They could have a reduced number of levels which only grant additional techniques, unarmed still governs accuracy and damage.
There have been some great enhancements to the crafting menu which deals with this exact problem. Most notably, bubbling up the most relevant things to the top of these lists. There’s no reason skills at 0, that you have no intention of advancing, have to appear on the first page of a multi-page stat page.