In a blender or food processor, whirl cilantro, garlic, ginger, chiles, garam masala, cumin, and 1/4 teaspoon cayenne into a smooth paste, adding 1/3 to 1/2 cup water as needed to facilitate blending. Taste and add more cayenne, if desired. Scrape into a bowl.
Shortly before serving, rinse shrimp; drain well. Add to marinade with oil and salt; mix well. Thread shrimp onto 6 to 8 metal skewers, piercing them through the center so they lie flat in a row.
Lay shrimp skewers on an oiled grill over a solid bed of hot coals or over high heat on a gas grill (you can hold your hand at grill level only 2 to 3 seconds); close lid. Cook, turning once, until shrimp are opaque but still moist-looking in center of thickest part (cut to test), 3 to 5 minutes per side. Transfer to a platter and serve with lime wedges and mint chutney.
Ground toasted cumin: In a 6- to 8-inch frying pan over medium heat, stir 2 tablespoons cumin seeds often until lightly toasted, 2 to 4 minutes. Whirl in a blender until finely ground. Makes about 2 tablespoons.