1. Combine the juices, oil, marmalade, ginger, and cilantro in a shallow glass or ceramic dish. Season with salt and pepper, whisking well. Pour half the mixture into another bowl and set aside. Add the chicken to the dish, turning several times to coat. Cover and refrigerate for at least 1 hour and up to 6 hours.
2. Prepare a charcoal or gas grill. Lightly spray the grill rack with vegetable oil cooking spray. The coals should be moderately hot to hot.
3. Lift the chicken from the marinade and let most of it drip back into the dish. Grill the chicken for 12 to 16 minutes or until cooked through, turning several times; brush with any remaining marinade during the first 5 minutes of grilling. The chicken is done when the juices run clear when the thickest sections are pierced with a fork or sharp knife. Set aside to cool slightly.
4. Holding the fruit above a bowl, separate the orange and the grapefruit half into sections, letting any juices collect in the bowl. Drop the sectioned fruit into the bowl, add the scallions, and pour the reserved orange marmalade dressing over the fruit. Toss gently. Cut the chicken into bite-sized pieces and add to the bowl. Toss to coat and season with salt and pepper.
5. Arrange the lettuce and arugula on a platter and top with the chicken mixture. Garnish with radishes and cilantro and serve.