For dressing, combine salad oil, vinegar, sesame oil, soy sauce, mustard, and crushed red pepper in a screw-top jar. Cover and shake well to mix.
Stir together red cabbage and bok choy; divide among eight salad plates. Top each with pineapple, sugar snap peas, mushrooms, and cut up radishes. Drizzle dressing over salads. Garnish with whole radishes.