Prepare the dipping sauce: In a small pot over medium heat, combine 1 cup water, rice vinegar, ketchup, sugar, and 1/8 teaspoon salt. Bring to a simmer.
In a small bowl, whisk the cornstarch with 3 tablespoons of water until smooth. Pour this slurry into the simmering sauce, stirring constantly until thickened. Remove from heat and set aside.
Clean the shrimp and pat dry. Using the flat side of a cleaver or a heavy skillet, gently smash each shrimp to flatten it slightly. Season with a pinch of salt and white pepper.
Using kitchen shears, cut each round rice paper sheet into 4 equal triangular quarters.
Assemble the chips: Place one quarter of dry rice paper on a flat surface. Place a flattened shrimp in the center. Cover with a second quarter of dry rice paper. Press down firmly around the shrimp; the natural moisture of the shrimp will bind the two sheets together.
Heat the oil in a wok or deep skillet to 375°F (190°C).
Carefully lower the chips into the hot oil, a few at a time to avoid overcrowding. Fry for about 1 minute, flipping halfway, until the rice paper puffs up white and crispy and the shrimp turns pink.
Remove with a slotted spoon and drain on a wire rack or paper towels. Serve immediately with the sweet and sour sauce.