Whisk 1 tablespoon vegetable oil, 1 teaspoon ginger, and crushed red pepper in bowl. Add shrimp; toss. Chill 2 hours.
Whisk 2 tablespoons vegetable oil, 1 teaspoon ginger, lime juice, and soy sauce in another bowl. Add rice, mango, and onions; toss well. Cover rice salad; let stand at room temperature.
Boil sugar snap peas in salted water until crisp-tender, about 1 minute. Drain peas and transfer to medium bowl. Toss peas with sesame oil and sesame seeds.
Prepare barbecue (medium-high heat). Thread 4 shrimp onto each of 4 skewers. Grill shrimp until just opaque in center, about 2 minutes per side.
Mound rice and mango salad in center of large platter; surround with sesame sugar snap peas. Top with grilled shrimp skewers and serve.