Same with that. They moisten and sooth the skin, they won't make the poop stick worse. If it's getting stuck in feathers and making things worse, you can trim back those feathers with some scissors to help it stay cleaner (looks like maybe you have done that some). They'll grow back when she molts. If she's having a lot of runny droppings that are causing it to happen all the time, maybe need to look into that. Could be diet, internal parasites, age. How old is she? Sometimes older hens will start getting issues with dirty butts, and it could be that they are a bit stretched from years of laying and don't push droppings out as well, or could be a reproductive problem making it harder for them (that is less likely since you say she is laying). As well as the other things mentioned.