Heat 1/2 tablespoon of the oil in large nonstick skillet over medium heat. Add red pepper; cook for 4 minutes. Add green onion; cook 2 minutes more. Remove from heat.
Whisk together mayonnaise, lemon juice, egg, egg white and mustard in medium-size bowl. Stir in red-pepper mixture, fresh bread crumbs and crab.
Place dry bread crumbs in pie plate. Shape crab mixture into eight 4-inch patties, using about 1/3 cup for each. Coat both sides of patties with crumbs.
Wipe out the skillet with paper toweling. Heat half of remaining oil in skillet over medium-low heat. Add crab cakes; cook for 5 minutes or until crispy-browned. Flip cakes over. Add remaining oil to skillet; cook 5 minutes more or until crispy-browned. Serve with fresh lemon wedges or tartar sauce.