Puree cucumber with vinegar in a blender until very smooth. Add sesame oil and blend until emulsified. Season with salt and pepper.
Pat shrimp dry and sprinkle with curry powder, salt and pepper, to taste.
Heat 1 tablespoon vegetable oil in a 12-inch nonstick skillet over moderately high heat until hot but not smoking, then saute shrimp in 2 batches, turning them, until golden brown and just cooked through, 2 to 3 minutes. (If necessary, add more vegetable oil to skillet for second batch.) Transfer shrimp to a plate to cool.
Serve shrimp at room temperature with vinaigrette for dipping.
