Not for the rank novice or technically challenged, but I've adapted a cleaning process which is used for telescope mirrors: Remove mirror from camera (easy on Zenit. Alpa, some Rollei TLR, etc). While holding the mirror under a stream of fresh water from the tap, wet your fingers with a bit of dish soap, then lightly scrub surface of mirror with those wet fingers. Always make sure that there's a film of soapy water between your fingers and the mirror's surface. When it looks good, rinse, and gently dab away any remaining droplets of water while minimizing contact with the mirror's surface as much as possible. I've achieved pristine, streak-free results in this manner.
I've also had success cleaning mirrors in situ via other methods, but I'd be very, very careful about tissue wrapped around a stick: That may be fine in the hands of a trained technician, but even then, it's super-easy to overestimate the amount of pressure you can safely apply