Wet sand to 2000, use the steel wool on your desired area followed by an automotive polish over the areas your thumb won’t need to come into contact with.
On my last poly neck I stopped at 2000 wet sand and then polish the heel and headstock.
Up to you, but steel wool treatment removed the ‘contour map’ appearance which you’ll have an probably stand out more as yours is a dark colour. I don’t know of, or heard of, any restrictions due to the oil base.