For more of an extreme, you could try the methods suggested on the following page:
• Mighty Mouse - gutting and cleaning: (for both USB and wireless, if you dare)
http://creativebits.org/toolbox/mighty_mouse_gutting_and_cleaning
Sounds almost like a course in taxidermy; the comment section covers other ideas
and it's best if you do not take the unit apart. My USB wired Mighty Mouse (or Apple
USB rollerball mouse) was an easy clean - however be sure to keep the keys on the
keyboard clean too, or any contamination will simply transfer back to the roller ball.
I use vinegar-based window cleaner; works OK on other surfaces too, if in moderation.
Try paper towel, a dampened area, then roll it in all possible directions and then back
over a dry area. I seldom unplug mine from the Mini, & do not shut the Mac off either.
...Also try a different finger on the roller ball. You may want to sandpaper your finger...!
My mouse was acquired second-hand and cost me 50¢ from a thrift store bin; it's an
official Apple mouse. I cleaned it up before trying it, this was after buying a newer Mac
with much later OS X than I'd been using; a scroll-wheel mouse is a near necessity in
the later OS X versions. I went from 10.5.8 to 10.9.5; and the first day, I had to buy a
'mouse-in-a-box' for $12. at a grocery store ~ or take the computer to an Apple Store or
the FedEx drop off, to return it, within days after buying it; the grocery was closer. The
Mac I bought did not ship with the OS X version I'd hoped; it was an online Apple Store
clearance model, and could've had any one of four versions OS X included.
{There used to be an even better web page (third-party) that had well-defined methods
of cleaning the mouse without take-apart, but the site is no longer hosted online.}
So the $12. 'mouse-in-a-box' is in use on my older G4 Mini (late 2005) since I'd been
using the original single button mouse, and have several spare keyboards + mice on
hand of that vintage. Figured it was handy to use the extra buttons in a newer mouse
instead of the contextual menu via keyboard. Actually the Mighty Mouse roller ball is
a bit small, though convenient for multiple direction scrolling; until it needs re-cleaned.
You can get a good condition as-new or slightly used looking pre-owned 'mighty-mouse'
from source online such as OWC macsales.com at discount, if you need a working spare.
Bluetooth example: http://eshop.macsales.com/item/Apple/MA272LLAC/ twentyfive dollars
USB example: http://eshop.macsales.com/item/Apple/MA086LLAC/ for nine dollars
In any event...
Good luck & happy computing!