Warm soapy water and an old toothbrush. G10 is fiberglass in epoxy, so it does not absorb water, does not swell, and shrugs off most solvents. For stubborn residue such as adhesive or tree sap, isopropyl alcohol is safe. Dry the knife afterwards for the pivot's sake, not the handle's.
The aggressive texture that makes G10 grip so well also traps grime, and wiping the surface with a cloth barely touches it. A brush is what actually cleans it.
Work the brush across the texture in both directions. Rinse and repeat if the water comes off dirty.
Isopropyl alcohol removes adhesive, sap and ink. Degreasers work too. G10 is genuinely chemically resistant and it is difficult to damage with anything you would have at home.
Avoid abrasives, which will dull the texture and leave shiny patches.
Dry the knife properly afterwards. Water in the pivot is the real risk in any wet cleaning, not the handle material. Work the blade, then let it air dry open before oiling the pivot.
See oiling a pivot.