I suppose it depends on what your yard/ garden looks like. If there are low spots where there are puddles you could always fill them in with stone, round pebbles that won't hurt the ducks feet.
I've seen some people use straw or wood chips in their duck run. It would probably have to be shoveled out at some point but you could always add it to a compost bin.
We use wood mulch in our run and it works well but we are not as damp where we are in the US.
View attachment 2496463
Your ducks are super cute, love runners!