In medium bowl, combine shrimp, 2 teaspoons soy sauce and 2 teaspoons cornstarch; let stand 5 minutes to marinate.
In separate bowl, whisk remaining soy sauce, remaining cornstarch, rice vinegar, hoisin sauce and ginger until blended.
In large nonstick skillet over medium-high heat, heat 1 tablespoon oil until shimmering. Add half of shrimp; cook 1 minute on each side. Transfer to clean bowl; repeat with remaining shrimp. Wipe out skillet with paper towel.
In same pan, heat remaining oil until shimmering. Add red onion, bell pepper and shishito peppers. Cook, stirring, 2-4 minutes until peppers begin to blister. Add vinegar mixture; cook, stirring, 1-2 minutes, or until sauce is slightly thickened. Add shrimp to pan. Cook, tossing well until shrimp and vegetables are coated with sauce.
Fill tortillas with shrimp mixture, cabbage and green onions.