In a bowl, mix shrimp, coconut milk, and 2 tablespoons sweet-hot chili sauce. Cover and chill at least 1 hour or up to 1 day (see notes).
Thread shrimp onto 8 to 10 soaked wooden skewers (see notes). Place on a rack in a 10- by 15-inch broiler pan.
Broil shrimp 3 to 4 inches from heat, turning once, until shrimp are opaque but still moist-looking in center of thickest part (cut to test), 5 to 6 minutes.
Arrange the cucumber slices on a platter. Set shrimp on top. Drizzle about 3 more tablespoons chili sauce over shrimp. Serve shrimp hot or cool with remaining chili sauce to add to taste.