Other useful 'tools' for rust/dirt removal are kitchen sponges with a coarse side for scrubbing pans, and nylon mesh scouring pads. Both can be used with mineral oil as a gentler substitute for fine wire wool.
The scouring pads can be cut into two or four pieces and used with a little cold bluing solution (rather than oil) to partially refinish small areas as light rusting is carefully scrubbed off. Any grease or oil obviously needs to be thoroughly removed first.