Preheat the oven to 500 degrees F. Season the hens all over with salt and pepper, place on a rack in a roasting pan and roast 15 minutes. Meanwhile, whisk the chili sauce, lime juice, brown sugar, olive oil and 2 teaspoons salt in a measuring cup to dissolve the sugar. Set half of the mixture aside in a bowl for the salad. Baste the hens with some of the remaining dressing, then rotate the pan and continue to cook until the hens are golden and a thermometer inserted into the thickest part of the thigh registers 160 degrees F, about 20 more minutes.
Meanwhile, peel and thinly slice the cantaloupe and shallot. Peel the cucumber, then halve lengthwise, seed and thinly slice. Toss the cantaloupe, shallot and cucumber with the reserved dressing. Divide the salad among plates. Use kitchen shears to cut each hen in half and place one half on each plate. Drizzle the pan juices over the hens and salad.