Same thing you would clean corrosion off a battery with: baking soda in water. it will clean it, but if the corrosion is deep, there's little you can realistically do. Moisture is no longer the issue now that it is already corroding, so WD40 won't help IMO. You can however put dielctric grease on it once cleaned to help prevent further corrosion.
Don't buy cleaning fluid, just replace the cable, providing it isn't an in wall run or something weird. Blue Jeans Cable and Monoprice have excellent cables and great pricing.