When I worked on farms, we used something called Virkon. It didn't produce nasty vapors like bleach, and had a good reputation for killing bacteria, fungi, and wiping out viruses (can't kill those because technically they are not alive - but that is another topic
)
Virkon comes in a powder (reminded me of Tang). Not drinkable!
I would mix up enough to clean off my boots before and after a trip to a farm, to prevent carrying anything unwanted.
I used to buy the large container, but you should not need that much.
Low-tech, you may just want to use something like detergent and hot water, followed with some vinegar and a change of bedding. Don't forget walls, if there are any. Then there are the alcohol-based products.
The feed store may have something they recommend.
One reason I don't promote the bleaches or vapor-producing chemicals is that I get an awful asthma attack around that stuff, so I reckon it may not be good for ducks, either.
It's work, I know, and what a time of year to have to do this. But, healthy happy ducks are worth it, I think.
Hang in!
By the way, if it just happens to turn out to be a fungal problem, Borax in hot water has been the best thing I ever used for mold and mildew.
