In the musical the king and i, the lead character sings about whistling when she feels afraid to hide her fear, which eventually makes her not feel afraid. the idea that acting like you are not afraid keeps you from feeling afraid is similar to which theory of emotion

I believe the answer is: James-Lange
According to  James-Lange, Emotions are created through the instigation fo physiological arousal.
He argued that by physiologically acting a certain way, our body would send a signal to our nervous system on the type of emotion that we need/desire and the nervous system would comply by creating that specific emotion.