Rather than a specific fighting style, I think you should generalize styles, and then allow players to role-play what style they actually know. Also, our system doesn't take into account that different practicers perform differently. When I wrestled, I wrestled completely differently than someone 2 weight classes below me.
Some boxers are aggressive (+ to Attack), others float like Butterflies (+ to Dodge)
Some Martial Artists always have their skills at the ready (+2 initiative) while others use their art mainly as a focus (+2 Will)
We can have just a general skill called “Fighting Style”. The player can call the style whatever they want as long as it is based in reality and existed at that time, or as long as it makes sense. They can assign it whatever bonus they want using 2 points… like +2 attack or +2 Dodge, or +1 Will and +1 Dodge or whatever.
Now the style is more than just a name on the paper, it's a part of the character and how the character fights. Two chaarcters who consider themselves boxers could have completely different bonuses.
We then allow the skill to be taken up to twice, independently of each other. The secodn time you take the skill, it works the same way, but the total bonus to any one modifier cannot be more than +3.
So now person A can have fighting style(Karate) while person B has fighting style(streetfighting). The skill would do 1 damage per hit… and we'll say maybe it raises to 2 damage per hit when you reach a skill of 8 in it.
Completely customizable fighting styles. Since players can name the fightign style what they wish and choose their bonuses to it, you will see less of these Martial Artists that make no sense because the player just wanetd the bonus, and more of a use of mainstream fighting styles such as wrestling, boxing, or streetfighting. Characters who take an Eastern fighting style will take it because it fits the character concept instead of for bonuses.