Preheat oven to 350°. Make chicken: Place flour in a shallow bowl, then season with 1/4 tsp. each salt and pepper. Place eggs and panko in two separate shallow bowls. Bread chicken, coating each tender first in flour, then egg, then panko.
Heat a large frying pan over medium heat and add 2 tbsp. oil. Working in batches, add several chicken tenders to pan and cook, turning once to brown on each side, about 5 minutes total. Transfer chicken to a baking sheet. Repeat with remaining tenders, then bake all in oven until no longer pink in center (cut to test), 10 to 15 minutes.
Meanwhile, make onigiri: In a medium saucepan, bring rice and 1 1/2 cups water to a boil, covered, then reduce heat and simmer 20 minutes. Remove from heat and let sit 10 minutes. Turn out onto a rimmed baking sheet and toss gently with remaining 1/4 tsp. salt.
Moisten your hands with water and divide rice into 4 balls. Re-moisten hands, then flatten each ball into a blunt triangle about 1 in. thick. Position base of 1 triangle facing you. Center 1 nori strip over rice, angling it diagonally from bottom left corner. Tuck ends around triangle. Repeat with second strip, working from the bottom right corner. Lay third strip at center of base of triangle, wrap it on an angle over rice, and tuck ends under.
Make ginger ketchup: In a small bowl, whisk together ketchup, soy sauce, ginger, and garlic. Set aside.
Divide chicken strips, onigiri, ginger ketchup, and snap peas between four bento boxes or compartmentalized lunch boxes.
Make ahead: The chicken and onigiri, cooled, then chilled airtight up to 1 day.