Squeeze cabbage to remove as much moisture as possible and place in large bowl. Chop the shrimp and pork together to mix. Add chopped onions, whole egg, cornstarch, soy sauce, sesame oil and oyster sauce to the cabbage. Add shrimp and pork mixture and mix until thoroughly combined.
To construct wontons, place one wonton wrapper on work surface with one point facing you. Mound one teaspoon of the filling in the bottom corner, about 1/2" from the edges. Moisten the edges with egg white. Fold the top corner over the filling, making a small triangle. Bring side corners together, overlapping slightly. Fold the top of the wonton over the wonton filling tightly, pushing out any excess that may have been trapped when it was covered. This is to ensure that the filling cooks completely and there is no residual oil trapped underneath the wonton wrapper. Firmly seal the edges of the wonton. Bring the side corners together overlapping slightly and pinch together firmly to seal. Place completed wontons on a large platter covered with wax paper. When you have filled all the wontons, cover the platter with a wet kitchen towel until you are ready to cook them.
To cook, heat a large container of peanut oil over medium high heat to 375 degrees. Drop one wonton into the oil and cook until golden brown, about 2-4 minutes, turning once during the cooking process. Remove and drain thoroughly on paper towels. The first wonton will not be as nice as the remainder. When you have removed the first wonton, you may cook the rest of them in batches of 8-10.