While skewers soak, cut onion wedges in half lengthwise. Combine onion and next 3 ingredients in a large bowl. Add 1/2 teaspoon cumin, 1/4 teaspoon salt, and 1/4 teaspoon pepper. Cover and marinate in refrigerator 15 minutes.
While chicken and onions marinate, combine remaining 1/2 teaspoon cumin, remaining 1/4 teaspoon salt, remaining 1/4 teaspoon pepper, yogurt, cucumber, and green onions in a bowl. Cover and chill until ready to serve.
Thread chicken and onions alternately onto skewers; discard marinade. Place skewers on grill rack coated with cooking spray. Grill 15 minutes or until chicken is done, turning often. Serve with yogurt-cumin sauce.