Butterfly shrimp by cutting almost, but not all the way, through backs. Toss with garlic, oil, and lime juice. Season with salt. Marinate, chilled, 1 hour.
Gently press 1 shrimp open and thread lengthwise onto a skewer near pointed end. Repeat with remaining shrimp and skewers.
Arrange sates in a row on 1 long side of a broiler pan so that blunt ends of skewers point toward middle of pan. Cover exposed portions of skewers with a sheet of foil (don't cover shrimp). Arrange another row of sates over foil. Continue adding rows of sates and layers of foil until pan is full, making sure exposed skewer ends of last row of sates are covered with foil.
Broil until shrimp are just cooked through, 3 to 4 minutes. Serve sates with chutney for dipping.
Drain yogurt in a fine-mesh sieve set over a bowl, chill, 1 hour. Cook coriander and cumin in oil in a small skillet over moderate heat, stirring occasionally, until fragrant. Coarsely chop chiles, then puree in a blender with drained yogurt, coriander mixture, and cilantro until smooth. Stir in lime juice, pistachios, and salt to taste.