To prepare flavored mayonnaise, combine first 6 ingredients in a small bowl; cover and chill.
To prepare salmon cakes, heat 1 teaspoon oil in a medium nonstick skillet over medium heat. Add onion and celery; sauté 4 minutes or until tender. Combine onion mixture, 1/2 cup crackers, mustard, 1/4 teaspoon black pepper, salmon, and egg in a medium bowl. Divide salmon mixture into 4 equal portions, shaping each into a 1/2-inch-thick patty. Coat each patty with 1 tablespoon crackers. Cover and chill 20 minutes.
Heat 2 teaspoons oil in a large nonstick skillet over medium heat until hot. Add patties; cook for 5 minutes on each side or until lightly browned. Serve the salmon cakes with flavored mayonnaise.