If shrimp are frozen, thaw them in the refrigerator or under cool running water. Remove shells while keeping tails intact. Rinse and pat dry with paper towels. Place in a large bowl.
In a small bowl, combine coconut milk, lime zest, lime juice, sugar, green curry paste, fish sauce, and ginger.
Pour about half the coconut mixture over the shrimp in the bowl. Cover and refrigerate for 30 minutes, stirring once halfway through. Keep the remaining coconut mixture covered and refrigerated separately.
Remove shrimp from the marinade and discard it. Thread shrimp onto skewers.
Grill on medium-high heat for 5-8 minutes, or broil for 5-8 minutes, until the shrimp are opaque and cooked through.
While the shrimp cook, pour the reserved coconut mixture into a small saucepan over medium heat, bring to a boil, then simmer uncovered for 5 minutes.
Serve the shrimp with hot rice and coconut sauce. Serve with lime wedges.