I have not tried to clean one yet but according to the directions its says to wash them in soap and water. I would think soaking it in some Tide and then working in by hand a little would do just fine. I've use a consentration of granular Tide desolved in water to clean car engines, it should clean the snakes.
Presoak in a strong mixture of laundry or dishwashing liquid and water.
Then wrap'em up in an old sock or some such thing and toss'em in the washing machine. Presoaking prevents some of the funk from gettin in wifey poo's washer.
I have a bore snake for 6 different calibers .17 to 8mm. I clean them in the sink with laundry detergent, let them soak for an hour and agitate my hand. I make sure that they are rinced thoroughly and air dried. They come out fine.