Silver polish cloth will be fine...
Autosolve... Mask the fret board , a smear on the frets, allow a little time to darken / blacken - by the time you have done the last the first will be ready to polish off.
I use a little white mop on a dremmel, lowish speed, couple of passes back n forth across the width of the neck / length of the fret, not pressing down to hard...
Then a quick wipe with cloth, remove the tape, n clean the fretboard, lemon oil for wood, polish for laquered mapel.