If using bamboo skewers, soak in water for at least 30 minutes.
In a heavy-bottomed saucepan combine the sauce ingredients. Place over medium heat and cook (but do not simmer) just until the sauce is smooth and slightly thickened, 2 to 3 minutes, whisking constantly (the sauce will thicken further as it cools). Remove from the heat.
In a food processor or blender pulse the shrimp pop ingredients and process until a chunky paste is formed. Pour the vegetable oil onto a sheet pan and brush it evenly all over the surface. Using two spoons, shape the mixture into small ovals or quenelles, placing them on the oiled sheet pan as you make them. Turn them, making sure they are well coated with oil. Refrigerate for 30 minutes to 1 hour to firm up the texture.
Prepare the grill for direct cooking over high heat (450° to 550°F).
Place a quenelle on the end of each skewer. Brush the cooking grates clean. Grill the shrimp pops over direct high heat, with the lid closed as much as possible, until they are opaque throughout, 4 to 6 minutes, turning once or twice (cut one open with a sharp knife to test for doneness). Arrange the shrimp pops on a serving platter. Serve warm with the dipping sauce.