Remove all the strings, it makes for easier access and will allow you to clean the frets as well.
Just to clarify, the fretboard needs to be conditioned and cleaned, not polished. Make sure you do not use guitar polish for conditioning/cleaning, please use the proper products for such purpose - e.g. Dunlop 01 and Dunlop 02.
These can be purchased at Ranking/Swee Lee (Bras Basah) or Davis (Peninsular).