Depends on what you consider messy lol
Ducklings are messy. They play in their water in their brooder. That makes a big ol mess. But if you are aware ahead of time and take steps to minimize, it really isn't bad. I brood outside and that helps immensely. There are several threads on ways to cut down on water messes in the brooder. You basically want either a way to keep the water from getting out of the waterer to begin with or a way to contain it once it does get out.
I used puppy pads under the water dish at the beginning. Nobody was trying to eat them, so I wasn't concerned. After the first week or so, they were spending more time on the deck rather than in the brooder (other than at night), so water mess was on the deck and not an issue.
Keep your food and water a bit away from each other so they aren't dragging a mouth full of water to their food and making a mess and by the time they get to the water dish, most of the food is not longer stuck to their bills to get in the water.
Once they are in their coop (and you can brood in the coop as well), it depends on the coop to how to manage water.
I don't put water in the coop once they are old enough to not need food and water available all the time. If it is hot at night (much of summer), I may provide water. I hose the coop out daily, so if they make a mess over night, eh, no biggie for me.
I built a 11x7 raised pond for my girls. Any splashing they do just waters the plants next to the pond. Their pen has dish of water on a block so they don't hop into it. This summer when they have to be penned up, I will use a kiddie pool and dump every other day - that will water the plants around the pen and any grass that hasn't died yet.
I have a large yard they free range in, so I don't notice holes they make when they are drilling for bugs or bare spots or things like that that result because they are in a smaller space. When it rains and we have a lake in the yard, there are gobs of puddles, so they don't focus on just one, they play in all of them, so once dry, I never know there was a duck puddle there.
A lot of duck mess is how to manage it.
I don't have cayugas or know anybody that does to be able to comment on them.