Preheat oven to 450°F. Place a wire rack on a rimmed baking sheet. Stir panko and oil together in a wide shallow bowl or pie plate. Toss chicken with 1 tablespoon mayonnaise in a medium bowl until thoroughly coated.
Working with 1 piece at a time, dredge the chicken in the panko mixture to coat. Transfer the coated chicken pieces to the prepared rack, spacing the pieces evenly apart. Discard any remaining panko mixture. Bake the chicken until an instant-read thermometer inserted into thickest portion registers 165°F, 10 to 12 minutes.
Meanwhile, whisk chili sauce, lime juice, Sriracha, onion powder and the remaining 1/3 cup mayonnaise together in a small bowl until blended.
Transfer the chicken nuggets to a large plate; sprinkle evenly with salt. Drizzle with 1/4 cup of the sauce. Serve with the remaining 1/4 cup sauce for dipping.