I would NOT use listerene it contains THYMOL and as with most antiseptics ending in OL it is a derivative of phenol. Reptiles are especially sensitive to phenols much more than mammals. I would avoid using a phenol based anything around them this is where the pine wood chip debate comes from and listerene certainly contains more phenols than pine wood does (likely more than cedar) the second part of this is why do anything at all. It is a pointed disinfectant to kill 'germs' that cause gingivitis and bad breath. Not those that cause infection or much else human mouth germs are not likely to be found on surfaces or in a snakes mouth as the body temps are different.
If you must use a home remedy (I would suggest a vet not some half baked home method) Maxi guard oral cleansing gel with no alcohol or a chlorhexidine oral rinse.