For the filling: Place the tuna on a cutting board. Remove the skin, if any, and dice the fish into 1/4-inch cubes and place in a large bowl. Mince the ginger and green onions and add to the tuna. Blend in the egg whites, wine and the soy sauce. Toss, and chill in the refrigerator for 30 minutes.
To assemble: Keep a cup of water, your filling, and your wrappers handy. Lay a few wrappers out flat on a countertop. Place about 1-ounce of filling into the center of a wrapper using a tablespoon. Dip your finger in the water (or use a wet brush) and run your wet finger (or wet brush) along 2 connected edges of the wrapper. (Say, for example, the left side and the bottom.) The area you are creating here is a moist strip along the half of the perimeter where water is applied. Fold the wrapper over on the diagonal. The 2 moist sides will bond to their dry counterparts to make a nice little triangular pocket. Remember that the water acts like a glue. Thus, if wet edges are folded to the dry edges, all is well; otherwise, your pot stickers will come open. (If you get pulled away in the process of assembling, cover the wrappers with a kitchen towel to keep them moist until you get back.).
To give the folded-over wrappers that traditional pot sticker look, pick up the wrapper and fold over the sides that have been joined with water in a pleating action. Make 3 or 4 pleats. Put the assembled wrappers on a parchment-lined pan, but make sure that they do not touch each other. If they are left touching, they will stick together, which is bad news because, when you go to separate them, you will have pot stickers with holes. However, this is less of a problem if you use traditional pot sticker wrappers, as they are thicker. When all of the pot stickers are assembled in wrappers, you can cook them immediately at this point or you can freeze them for future cooking. We use to freeze them by the hundreds at the Diner, placing them in airtight containers more suited for freezer storage.
For the potstickers: Heat a griddle, wok, or pan over medium-high heat. When hot, cover the bottom with nonstick spray. Put the potstickers in the pan and cover with a tight-fitting lid (or, if you are working on a griddle, use a pan to cover the pot stickers).
Lift the lid, toss in about a quarter of a cup of water, and quickly close the lid. Let the potstickers steam for about 4 minutes. If you really need to satisfy your curiosity and take a peek, just be sure to add more water. The end result should be that the pot stickers have a crispy golden brown bottom and a soft pasta top. We use to serve them at the Diner on a bed of garlic-sauteed spinach with a soy dipping sauce. (Chopsticks are provided.) I also recommend them with any good commercial spicy chili oil. To make the soy dipping sauce, mix equal parts soy and rice wine or black vinegar. Enjoy!