Preheat an outdoor grill or grill pan to medium-high heat. In a large bowl, whisk together the jalapeno, olive oil, cumin and 1/2 teaspoon salt. Add the shrimp and turn to coat. Grill the shrimp until just cooked through, 2 to 3 minutes per side; let cool. Halve the shrimp lengthwise.
In a large bowl, dissolve the brown sugar in the lime juice. Add the mangoes, cucumbers, radishes, scallions and cilantro; toss and season with salt. Add the shrimp and toss.