Exactly. As much as I love Chuck Norris and what he’s done for martial arts, Lee’s thinking and fluidity had way more impact in a shorter lifespan.
While some initial physical strength will be given to the MC if the player goes down the martial arts path, I’m more inclined to make it a speed-based skill. Speed and movement were the two greatest components that were drilled into us at the school I went to when I was in my early 20s.
I might also include some jiu-jutsu for takedowns as well. It won’t happen as often but it is another option. (Personally, I wish I had experience in Muay Thai or Krav Maga. )