I agree with Alex, no need to use a laser on these scopes, a film canister is the simple way to get it close enough.
You want to be very careful cleaning optical surfaces, easy to do more harm than good. Mirrors should only be cleaned if they really need it. There is an article here with some ideas on the procedure
http://www.iceinspace.com.au/63-345-0-0-1-0.html
When you put the mirror back, make sure you don't tighten the clamps, they should be sitting just above the mirror surface, to tight and even a small mirror can distort.
With Jupiter it is really low ATM and not very easy to observe. Even in my 20" the other night at about 2am it was a very more view with the atmosphere boiling away at low latitude. Neverteless you should be able to make out a disc and the 4 Galileas moons.
Malcolm