Place 1/4 cup all-purpose flour, 1 tablespoon cornstarch, 1 1/2 teaspoons kosher salt, 1/2 teaspoon dried oregano, 1/4 teaspoon garlic powder, and 1/4 teaspoon black pepper in a gallon zip-top bag and shake to combine.
Place 3 large egg whites in a shallow dish and whisk until frothy. Grate 4 ounces Parmesan cheese on the smallest holes of a box grater (about 1 cup), or measure out 1 1/4 cups store-bought grated. Place in a second shallow bowl, add 3/4 cup panko breadcrumbs, and stir to combine.
Trim the ends off of 1 pound zucchini. Slice the zucchini in half crosswise. Cut the pieces lengthwise into 1/4-inch thick planks. Working with two stacked planks at a time, cut all the planks lengthwise into 1/4-inch-wide sticks.
Heat an air fryer to 400°F. Meanwhile, bread the zucchini sticks in 3 batches: Add 1/3 of the sticks to the flour mixture and toss until evenly coated. Transfer the sticks, a few at a time, to the egg whites and toss to coat. Transfer the sticks to the panko and Parmesan and toss to coat. Place in a single layer on a rimmed baking sheet.
Arrange a single layer of zucchini fries in the air fryer basket, making sure they are not touching, about 12 at a time depending on the size of the basket. Coat with cooking spray. Air fry until golden-brown and crisp, 5 to 8 minutes. Remove from the air fryer and repeat with the remaining zucchini.
Serve immediately with ranch dressing, or place on a wire rack fitted over a rimmed baking sheet and keep warm in a 200°F oven until all the zucchini fries are ready.