Prep: 25 min., Chill: 30 min., Cook: 12 min. Make shrimp mixture up to one day ahead before forming into patties, if desired. Store in an airtight container in the refrigerator.
Stir together green onions, 1 tsp. garlic, 1 cup mayonnaise, egg, and next 5 ingredients in a large bowl. Chop shrimp, and add to bowl. Stir in 1 cup breadcrumbs until blended. Cover and chill mixture 30 minutes.
Stir together orange rind, orange juice, lime juice, remaining 1/2 tsp. garlic, and remaining 3/4 cup mayonnaise until blended. Cover and chill at least 30 minutes.
Shape shrimp mixture into 12 (3-inch) patties (about 1/3 cup each). Dredge patties in remaining 1/2 cup breadcrumbs.
Cook 6 patties in 2 Tbsp. hot oil in a large skillet over medium-high heat 3 minutes on each side or until golden. Repeat with remaining patties and oil. Drain on paper towels on a wire rack in a jelly-roll pan, and keep warm in a 250° oven up to 30 minutes. Serve with mayonnaise mixture, and garnish, if desired.