Soak wood chunks in water to cover at least 30 minutes.
Place tuna steaks in a large heavy-duty zip-top plastic bag. Stir together 2 quarts water and next 4 ingredients; pour over steaks. Seal bag; chill 3 hours, turning bag occasionally.
Remove steaks from brine. Wash and pat dry. Place on a rack to air dry 30 minutes. Brush with vegetable oil. Pat pepper on both sides of fillet.
Prepare charcoal fire in smoker; let burn 15 to 20 minutes. Drain wood chunks, and place on coals. Place water pan in smoker; add wine. Coat rack with cooking spray; place in smoker. Place steaks on upper rack; cover with smoker lid. Cook 3 to 4 hours or until fish flakes easily when tested with a fork.