Although James Brown's leg was somewhat sore, the pain was nowhere near that level. By exaggerating it, firstly, he was teasing Joan with the ulterior motive of taking advantage of her. Unlike with a girl like Sarah Utah, James Brown wouldn't dare fool around, but with someone like Joan, although he didn't want to start anything serious, taking a small advantage didn't weigh on his conscience at all.
Additionally, James Brown acted this way to prevent Joan from ever noticing from his physique and gaze that he was the same person as the Mysterious Figure. By letting her think he was weak, even if she noticed something off, she wouldn't connect him with the Mysterious Figure.
Thirdly, since those guys had hired people to take care of him, it was inconvenient for him to strike back directly at that moment. Naturally, he had to pretend to be injured, letting the other party break the bank a bit. Now that he had the police backing him up, it would be a waste not to trick them.
