Preheat oven to 450 degrees F.
Cut each zucchini into pieces 3 inches long and then into quarters. Set aside.
In a shallow dish, mix together the bread crumbs, Parmesan, oregano, basil, salt, and black and cayenne peppers until well mixed.
In the bowl of a mixer, whip egg whites until just frothy and then pour into a separate shallow dish. Coat zucchini sticks with egg white and then roll in bread crumb mixture until completely covered.
Place a wire rack on top of a baking sheet. Arrange the coated zucchini on the wire rack, about 1-inch apart from each other. Spray lightly with cooking spray. Bake for 7 minutes or until crispy. Serve immediately.