For the filling: Mix the shrimp, chives, water chestnuts, oyster sauce and rice wine into a bowl and sprinkle with salt and pepper. With clean hands, squeeze the filling through your fingers so that all the flavors are combined well. Wash your hands and dry well. For the dipping sauce: In a small bowl, combine the soy sauce, rice vinegar, sesame oil and cilantro and set aside.
For the potstickers: Sprinkle a baking sheet or plate with some cornstarch. Then place a dumpling wrapper in the palm of your hand. Place a heaping teaspoon of the filling in the middle of the dumpling skin. Then dip your finger into a water bowl and brush around the rim. Fold in half so you have a half moon shape, pressing down on the edges to make sure the dumpling wrapper sticks together well. Pleat the edges of the potsticker 4 times, pinching well to secure. Place the potstickers on the prepared baking sheet until ready to cook. (You could make ahead to this point and freeze in an airtight container, then cook from frozen when desired.) Heat a wok over medium heat. Cook the potstickers in two batches, so you don't over-crowd the pan. Add 1 tablespoon of oil and arrange half the potstickers standing up in the oil. Cook, uncovered, until the bottoms are pale golden, 1 to 2 minutes. Add 1/4 cup water around the edges of the wok, then cover and cook until the liquid has evaporated and the bottoms of the potstickers are crisp and golden, 5 to 7 minutes. Repeat with the next batch. Serve alongside the dipping sauce.