Mine were pretty dry once I figured out how to make a splash catcher.
What has worked best for me (after trial and error and upgrade as they have grown) is:
*A waterer they cannot get in or tip over (chick waterer)
*Plus, a face washer they cannot get in or tip over (plastic tub with snap on lid and a hole cut out just large enough for a head and a half)
*A shallow bucket, about head high, with one section of one side cut down and a ramp or other means to safely enter and exit
*compressed sawdust pellets or towels in the bottom of the shallow bucket to absorb splash (or a perforated platform with a fitted pan underneath that they cannot stick a foot through and break a leg)
The shallow bucket needs to be large enough to hold the drinking water, face wash, and at least half the little bodies that will be using these.
I used towels with the ducklings, and the sawdust pellets with my grown ducks - if you are concerned they might chow down on the sawdust pellets, you might cover them with some smooth, sturdy plastic mesh.
Maintenance is refilling the waterers and replacing sodden towels or sawdust or emptying the pan under the perforated platform.
My platform, by the way, when they were tiny, was a two piece broiler pan with the edges duck taped and a washcloth on top for no-skid.
So enjoy your ducks, they are waterfowl, and their water needs can be managed.