Just be careful with steel wool, especially the ultra-fine grades.
Tiny fibres of steel get hooked on the "oblique" ends of the grain and they WILL corrode over time.
This will leave nasty, odd coloured stains on the timber.
My trick to remove any "metal whiskers" is simple:
Get the meanest, most powerful "permanent" magnet to be found.
Wrap it in a couple of layers of CLEAN, cheese-cloth.
Glide the "non-scratch" magnet slowly along the grain of the stock (or antique table etc).
Inspect the cloth for little grey whiskers.
Reverse or replace the cloth and then run it in lines in the opposite direction.
Novelty and scientific supply folks sell small "super magnets" that are very handy for getting into nooks and crannies with this technique. (also useful for finding, picking up etc., small "feral" parts that leap off the bench. Sadly, these do not work on brass screws...........