My usual sermon on mirror cleaning :
Mirrors in Australia tend to get a pretty tenacious deposit of Eucalypyus oil and air pollution . There is no problem with starting off with a soak of methylated spirits on some paper towel layed over the surface and then a strong detergent solution with some pressure from a cotton wool bunch to cut through the grease.
If you breath on the mirror when it is dry and the breathe pattern looks all blotchy then you you still have grime and grease on the mirror .
Overcoated mirrors are tough - it is no different from cleaning your windscreen on your car- you wouldn't clean your windscreen would you if you were afraid of scratching it. ( I know that sounds sacrilegious but it is tru )
In my view people let their mirrors get into an aweful state and put up with low contrast views with loads of scatter around stars, and loss of planetary detail because they are afraid to touch the mirror surface .
So long as you wash off any loose grit that may have fallen on it there is no danger of scratching the actual mirror substrate in cleaning and little danger of putting scratches in the SiO or Quartz overcoat ( whichever it is ) . Coatings wont last forever anyway and neither will your eyesight
so why spoil your views with contrast destroying scatter due to dirt dust and grime .
If you can shine a light through the back of your mirror and see hundreds of obvious pinholes then you need a recoat .