Line cookie sheet with cooking parchment paper; line serving platter with paper towels. In food processor, coarsely chop shrimp. Add 1 tablespoon soy sauce, the lime juice, gingerroot, garlic and egg white; process with on-and-off pulses until well mixed. Gradually add 1 cup of the bread crumbs, processing with pulses until mixture is well blended. Remove shrimp mixture from processor; place in medium bowl. Stir in bell pepper and chile.
Divide shrimp mixture into 12 equal portions. Shape each portion into patty, 2 1/2 inches in diameter. Place remaining 1 cup bread crumbs on plate. Lightly press both sides of each patty into crumbs to coat evenly; place on cookie sheet. Refrigerate 20 minutes. Discard any remaining bread crumbs.
Meanwhile, in small bowl, mix wasabi mayo ingredients until well blended. Cover; refrigerate until serving time.
In 10-inch skillet, heat 2 to 3 tablespoons oil over medium-high heat about 2 minutes or until hot. Working in batches, cook patties in oil 8 to 12 minutes, turning once, until thoroughly cooked and golden brown. Remove patties from skillet to paper towel-lined platter; cover to keep warm. Repeat with remaining 2 tablespoons oil and remaining patties. Serve with wasabi mayo.