Cut a horizontal slit through one side of each steak to form a deep pocket; set aside. Combine wine and next 7 ingredients (wine through garlic) in a large shallow dish; stir well. Add steaks, turning to coat. Cover and marinate in refrigerator 30 minutes.
Remove steaks from marinade, reserving marinade. Sprinkle salt into pockets of steaks; set aside. Add arugula to marinade; toss well. Remove arugula from marinade; discard marinade. Stuff about 3/4 cup arugula into each pocket; secure each pocket with a wooden pick.
Prepare grill. Place swordfish steaks on grill rack coated with cooking spray, and grill 5 minutes on each side or until fish flakes easily when tested with a fork.