Heat grill or grill pan to medium-high. Rub chicken with half the oil, cumin, and 1/4 teaspoon salt; brush corn with remaining oil.
Grill chicken 5 to 7 minutes per side until thickest parts reach 165°F. Grill corn 8 to 10 minutes, turning frequently, until lightly charred and tender.
Rest chicken 5 minutes; cut into small cubes. Cut kernels from cob. Spread both in a shallow container; cool 10 minutes and promptly refrigerate.
Whisk yogurt, mayonnaise, jalapeños, lime juice, cilantro, scallions, and remaining salt. Fold in cooled chicken and corn; refrigerate 30 minutes.
Broil cut bagel faces 1 to 2 minutes; cool. Place one dry lettuce leaf on each bottom; divide salad evenly on top.
Close and halve. Serve cold or refrigerate in covered containers until lunch, assembling near serving for best texture.