Preheat oven broiler. Heat a large skillet over medium-high heat. Add oil to pan. Add ginger; cook 1 minute.
Sprinkle shrimp with 1/4 teaspoon salt. Add shrimp to pan; cook 3-4 minutes or until done. Keep warm.
Arrange buns in a single layer on a baking sheet, cut sides up. Broil 45 seconds or until toasted.
Combine celery, sour cream, mayonnaise, shallots, and lemon juice in a medium bowl; stir in remaining 1/4 teaspoon salt and pepper. Place 1 Romaine lettuce leaf and red cabbage on each bun. Top with 1 tablespoon sour cream mixture and 3 shrimp. Cover with top halves of buns.