Pour vegetable oil into a medium saucepan until 1-inch deep and place the pan over medium heat. Let the oil heat for about 3 minutes. As the oil heats, cut each wonton wrapper into 4 equally square pieces. Very carefully drop the squares into the hot oil 1 at a time, working in batches of 4 at a time. The wontons will bubble up and turn golden brown very quickly. Remove them with a slotted spoon to a piece of paper towel and repeat the process until all of the wontons are fried.
The wontons may be fried 1 day in advance and stored in an airtight container.
Pour the soy sauce into a large bowl and whisk in the ground ginger, cilantro and green onion. Next, cut the tuna into 1-inch square strips and place them in the marinade. Set aside for 15 minutes.
Place a large heavy bottomed skillet over high heat for 3 minutes. Spray with cooking spray and immediately place the tuna strips in the pan, searing each of the 4 sides for 30 seconds only. Remove from the pan and set aside.
To assemble, place a small amount of the relish on a wonton crisp. Carefully slice the tuna strips into 1/4-inch pieces. Place 1 piece of tuna atop the relish and serve.
*Wonton crisps can be made several days in advance and kept in an airtight container.
Place all the ingredients in a bowl and mix well. Refrigerate for 30 minutes to macerate.