GoJo is a brand name but "waterless hand cleaner" will remove petroleum based grease/oil quite effectively. The key to using the stuff is in the nomenclature - waterless. Do all the scrubbing without water, then use water to rinse it off.

Different chain lubricants are more/less messy. Wax based lubes clean up easier but I don't think they suite a wet environment.

The key as others have mentioned is, don't bump the chain.