Wash hands with soap and water.
Gently rub produce under cool running water.
Mix together prepared zucchini, cabbages, onions, and radishes in a large bowl.
In a separate small bowl, mix together mayonnaise and pepper.
Toss vegetables with dressing.
Chill at least one hour before serving
Adapted from recipe Zucchini Coleslaw, from www.usda.gov/whatscooking