You don't need to use any rigid bodies, or mesh colliders to accomplish what you are trying to do.
Street Fighter like games are usually done with bounding boxes, now based on whether you want 2D or 3D collision, you make the boxes 2D or 3D. In unity just set the 'z' size of a box collider to 0, for 2D and for 3D you can manipulate the z based on how wide your model's appendages are (arms, legs, torso, etc..)
Write a simple AABB collision detection, as your broadphase, and process your animations, action, reactions, based on this result.
Am not sure but, I guess if you wanted to use forces at exact collision points, you won't have to process your narrow phase, just grab contact point from Unity itself, and you could use rigid bodies, and toggle between isKinematic. But I don't think that's required.
Street Fighter, and games alike are heavy in terms of their AI, and managing their attack and defensive strikes, with the use of a FInite State Machine (FSM), the responses are handled solely by the animations based on who's hurt box has collided with who's hit box first.