FYI, chlorhexidine is also a common ingredient in (human) mouthwash, & I can recall someone saying they just used mouthwash to clean their cages...
But personally I don't want a minty-fresh or cinnamon-flavored pet, and I wouldn't assume the other ingredients are OK left in the cage...

I've bought chlorhexidine online*- from farm suppliers- and you should be able to find or order it thru your nearest feed store too, though they might only carry
it in gallon size jugs. *I bought a 16 oz. bottle "Durvet" brand. You can of course use it for household cleaning too, but a gallon will still take a LONG time to
use with the dilution rate for snakes, lol. Might even check with a pharmacy, but they might charge more for it?