Keeping those holding tanks safe and healthy (potable water and waste water) is important, and not something to experiment with. I'd be concerned that just because you know you're
not planning to drink that water that someone else doesn't come along and take a drink from the tap, or drink some shower water.
Chlorine can be a nasty customer when used incorrectly, but unless you know for sure that something else will be as effective, I'd be careful experimenting. I'd suggest you consult one of the big stores that deals with RV products, like Camping World (there is one in Fort Worth, on the sorth side of town) http://www.campingworld.com/
If there is a safe non-chlorine product to use to keep that tank clean, they'll probably have some in stock or be able to order it for you.
Good luck, and safe travels!