To prepare rémoulade, combine first 9 ingredients in a bowl; cover and chill.
To prepare croquettes, combine 1/3 cup yogurt, 1 tablespoon mustard, and egg whites in a bowl. Set aside.
Heat a nonstick skillet over medium-high heat. Coat pan with cooking spray. Add 1/2 cup onion and celery; cook 4 minutes or until tender. Cool slightly. Combine onion mixture, yogurt mixture, 1/2 cup crackers, 1/4 teaspoon dried tarragon, 1/8 teaspoon pepper, and salmon in a bowl; toss gently. Cover and chill 10 minutes. Divide salmon mixture into 8 equal portions, shaping each into a 1/2-inch-thick patty. Coat patties evenly with remaining 1/2 cup crackers. Cover and chill 20 minutes.
Combine carrot and 1/4 cup rémoulade in a bowl (reserve remaining sauce); toss gently to coat.
Melt butter in a large nonstick skillet over medium-high heat. Add patties; reduce heat to medium. Cook 4 minutes on each side or until lightly browned. Serve croquettes with carrot salad and remaining sauce. Garnish with fresh tarragon, if desired.
