Heat the vegetable oil in a large heavy-bottomed pot until it reaches 350 degrees F.
In batches, carefully lower the wrappers into the hot oil and fry until golden brown, 1 to 2 minutes. Remove to a paper towel to drain, sprinkle with salt and set aside.
Preheat the oven to 350 degrees F.
Put the cream cheese, milk, sriracha, brown sugar and soy sauce in medium bowl. With a hand mixer, beat together until smooth, about 1 minute. Fold in the shredded crab meat, cheese and scallion whites. Taste and adjust the seasoning as needed.
Transfer to a small baking dish and bake until bubbly, 20 to 25 minutes. Sprinkle with more cheese, some paprika and the scallion greens. Serve with the fried wonton chips. (If not serving right away, cover the dip with foil to keep warm.)