In a medium bowl, mix 1/4 cup lemon juice, the olive oil, 2 tbsp. ginger, 1 1/2 tbsp. garlic, 3/4 tsp. salt, the sugar, and 1/2 tsp. chile flakes. Add shrimp and mix to coat. Cover and chill about 1 hour, stirring once or twice.
Meanwhile, combine mayonnaise, remaining 1/4 cup lemon juice, 2 tbsp. ginger, 1 1/2 tbsp. garlic, 3/4 tsp. salt, 1/2 tsp. chile flakes, and 1 cup cilantro in a food processor. Whirl until smooth. Scrape aioli into a small bowl, cover, and chill until ready to use.
Preheat grill to medium-high. Lift shrimp from marinade (discard any remaining marinade), and thread onto metal or soaked-wood skewers, interspersing with cherry tomatoes. Grill kebabs (close lid if using a gas grill), turning once, just until shrimp is opaque but still moist-looking in center of thickest part (cut one to test), 3 to 4 minutes total.
Transfer kebabs to a platter; garnish with lemon wedges and cilantro sprigs. Serve with cilantro-ginger aioli.
*We use shrimp often labeled "jumbo" (21 to 25 per lb.). If you use smaller ones, reduce the grilling time slightly.
Note: Nutritional analysis is per serving with 2 tbsp. aioli.