If you'll go to your local hardware store and pick up "oooo" steel wool, that will work just fine. Although it is okay to use it on the fretboard as well as the frets, I don't want any of those tiny parallel scratch marks on the board along the frets, so I tear off two pieces of masking tape, place them on either side of the fret, make anywhere from 18-24 passes along the fret, then move the pieces of tape to the next one until I'm done. Your frets will look marvelous when you're done. May take you fifteen minutes tops.
I read about this method years ago on some website, and have used it on beater guitars as well as fine concert guitars with no problems. Michael.N. is right--there is a little cleanup involved, but it amounts to basically holding the guitar over a large trash can and blowing the tiny pieces of steel wool into it. You might even use a shop vac if you have one. Then you can use the tape to pick up any remianing pieces you spot on the board.
Best of luck,