I would clean as though it were a full BP load. It may not be much, and the
smokeless will cause it to burn a lot hotter/cleaner, but the fouling residue
will still attract moisture* over the next several days.
Simple soap and water cleans it off
incredibly easily/quickly. Wash, dry, oil.
No need to go bananas at all.
*The residue itself is not so much "corrosive" as it is hy[g]roscopic.
Water held close to steel is not your friend.
