just take it out and clean it

ive never needed to use cotton buds on my mirrors. i pretty much do the same as in Mikes article so follow that for the bits i dont describe
1) rinse all the loose bits off under the tap
2) fill the sink with luke warm soapy water
3) let the mirror soak for however long you think it needs
4) give it another blast under the tap.
if theres anything still on there, repeat till its gone. I never had to do it more than 3 times even with some pretty solid gunk on there, remember to give it a final rinse with distilled/demineralised water
remember: you can only damage your mirror if you touch the surface, solution = dont touch the surface (with anything). simple eh
just be very careful getting it out of the cell, the mirror will be a lot heavier than you first expect and it will more than likely be stuck to the cell with double sided sticky foam pads so take your time.