id rather add it to the tip of a weapon so they get infected if they live.
Be careful not to cut yourself with your awesomely sharp sword of a thousand serates after you coat it with septic nastiness. I certainly wouldn't want to be the squire tasked with cleaning your equipment after battle, so you probably wouldn't have many stableboys volunteering to deal with your weaponry.
Not sure of the best way to handle infection vectors and nastiness of wastes, but bacteria and fungus and algae blooms can consume wastes. Other vermin such as dung beetles and flies and misquitoes slowly consume waste as well, handling your filth could be very fun.
If you don't have a proper latrine/outhouse/sewage system, not only would the resulting bacteria and growths begin to infect your dwarfs slowly, you could easily begin to see your fortress overwhelmed with swarms of insects and greater numbers of vermin creatures.
Water flows would definitely help to flush highly concentrated collections of waste downstream, but management of residual sludge would begin to be necessary. If you can seal a system, the vermin will remain concentrated in the sewer areas, and fixtures like toilets and commodes and such would act as seals. If you could add yeast or something similar to rid-x to your sewers, you could begin to have somewhat clean sewers that wouldn't yield ferocious swarms of flies through your fortress.
If yeast is ever required for brewing dwarven spirits, it could serve a secondary role of keeping the mighty shit tunnels of the Mountainhome clean of disease and vermin infestations. If you so desire, you could build a megaproject around the idea of having a waste cistern that you keep a live bacteria and fungal cultural growing threw periodic flushing of the enitre dwarven sewer system.