In a sieve or colander, drain zucchini, squeezing to remove excess liquid. Pat dry. In a small bowl, combine the zucchini, onion, bread crumbs, eggs, salt and cayenne. Gently stir in chopped egg whites.
Heat 1 tablespoon oil in a large nonstick skillet over medium-low heat. Drop batter by scant 2/3 cupfuls into oil; press lightly to flatten. Fry in batches until golden brown on both sides, using remaining oil as needed.