This is a character's choice (producers decision) related to the state of the scene he is doing.
You already pointed out in the question:
He always wore white shoes, except when he found the chemist and in tournament when he wore black shoes without the suit.
It seems that he whore white shoes in casual and business environments, the shoes being white transpiring calm and relaxing environments.
And black when he was going into action, traspiring a more violent e serious environment.
Colors scheme (tones) are sometimes used in movies to explain and transpire emotions to the audience.
Color can affect us psychologically and physically, often without us being aware, and can be used as a strong device within a story. Knowledge gives you control, and control means you can manipulate and use color to give your work a powerful and beautiful edge.
Being able to use color to create harmony, or tension within a scene, or to bring attention to a key visual theme can be used to spectacular effect.
It also could be just preferences. I also wears a type of shoes in casual, business environments, and some other different shoes when doing hard work or exercising.