Combine first 6 ingredients in a medium bowl. Add shrimp; toss to coat. Cover and chill 1 hour.
Bring water and coconut milk to a boil in a medium saucepan; add rice. Cover, reduce heat, and simmer 15 minutes or until the liquid is absorbed. Add carrot and next 7 ingredients (through salt); tosss gently to combine.
Prepare grill or grill pan to medium-high heat.
Thread 3 shrimp onto each of 12 skewers. Place skewers on grill rack or grill pan coated with cooking spray; grill 3 minutes on each side or until shrimp are done. Serve skewers over salad.