Any abrasive method -steel wool or whatever, even a cloth with a cleaning agent - is going to increase wear on edges, corners and the most exposed surfaces, while totally failing to reach right into recesses.
That is why using the electrolysis method is IMOH the best way to preserve the steel and any remaining bluing.

And since the electrolytic bath basically has the same effect as the expensive "degreasers/conditioners" sold for cold bluing, you can take a piece out of the electrolytic bath, brush off any loose particles with a stiff brush, flush in clean water, and dunk straight into the bluing bath. On rusted screws, for instance, electrolysis is an excellent way to clean up the threads. Try it on an old blued part or a rusted screw!