I would go to a laundry mat that has the big triple loaders. Do not dry clean , but that being said many "dry cleaners" have regular larger capacity washers that do not use the chemicals used in dry cleaning. They do not "dry" clean mens shirts .. they launder them. .. but using this kind of service you would not have control on the detergents used or the water temperature.
So best bet is find a laundry mat , and pick your own soap product.