I have a wooden wetroom how do i clean it?

I have a bathrooom which is made up mostly of dark varnished wood, I am renting so am not too sure as too how its put in or works ect. Obviously the bath is enamel but the panels all around are wood and the floor of the shower/wet room are made from the same wood. The problem I have is cleaning it usual bathroom cleaners leave a white residue as you shouldnt use them on wood and i dont think just water would be hygenic. Does anyone have any tips on how to clean or what products to use