Honestly, I'd just deal with the smell. If you clean very frequently, you can prevent too much stink. I had 4 ducklings in a brooder in my livingroom last winter. I cleaned that sucker 3-4 times a day - once before work, 2-3 times after I got home.
Can you bring in bits of whatever it is they eat outside?
And I use towels for my ducks when I have to crate them for whatever reason. Could you use paper towels, strips of paper, old t-shirts, clean shop towels, tree leaves? Do you have a heating pad for when they're on the balcony? Those...