Do you find that run of the mill sunglass cleaning sprays and cloths are OK?
Hi Greg, no don't do it like that on your primary mirror!
Do a search for "mirror cleaning" and there's a lot of threads discussing it with great advice in them.
I've been threatening to write an article on cleaning the primary mirror (i've even taken the pictures for it) but just haven't got around to it. I'll try and do it soon.
In the meantime, do a search... here's an example of the thread I was talking about
Some people will say "don't do it, it's better to leave it dirty than to risk scratching it". But i'm in the other camp - if it's dirty and needs cleaning, as long as you're careful and use proper precautions, the risk is very low.
Have a read, do some research, make sure your area is prepared and then go for it if you feel it needs it!