How can I clean sticky and dirty hand tool's rubber?
Rubber can usually be de-gunked with a good dishwashing liquid and a brush. Avoid abrasive sponges as they will abrade the rubber as well as the gunk. Products with citrus oils like lemon or orange oil will be very good at cutting really stubborn gunk; then you just wash off the oil with a detergent.

If you really want to recondition the tool, and you can replace the rubber, then go ahead; there will be more gunk and rust under the handle coating, and even completely clean the rubber will be roughed up from general use. For most pliers, you can just cut off the rubber, clean up underneath, and then get yourself a can of Plasti-Dip and re-dip the tool handles.