Combine first 5 ingredients in a small shallow bowl.
Place egg in a separate shallow bowl.
Trim ends from zucchini; cut each zucchini in half crosswise. Quarter each zucchini half lengthwise to make 24 zucchini sticks. Dip zucchini in egg; dredge in panko mixture; pressing to coat.
Place zucchini on a baking sheet coated with cooking spray. Coat tops of zucchini with cooking spray.