My duck did have wet feather, I took her to the vet, and the vet did not recommend dish soap. My understanding is that dish soap can be indicated in some circumstances, like if the bird has become water logged by an oil spill or an extremely filthy living environment. Then the soap removes the contamination, and allows the bird to reoil themself. If you give a soapy bath when it isn't indicated you risk removing natural preen oil and making the situation worse.
In my duck's situation her preen gland was fine, and I recommend that you look at your duck's preen gland. Touch it gently with your fingers and then rub your fingers together, they should feel a little bit slippery.
If your duck is disabled he might not be preening well and that could be why. My vet did x-rays and discovered that my duck had arthritis, so it was painful to preen well. For my duck we kept her warm, and dry. And also bathed her, with only water, inside daily to encourage preening in the bathtub. We had the water deep enough to get her off her feet. We had lots of soft bedding for her. When it was warm outside we misted her with a spray bottle set on the mist function. I often dried her with towels.
A vet is a great idea.