Hold Uni's tail up and move swiftly with a warm, damp paper towel and just wipe it off. I have to do that now and then. In fact, if there's a little dab left after her morning biz, Zoey assumes the poop position again and gives me a plaintive look until I get rid of it.
When her anal glands are full, she'll rub her butt on the rug and give me that same intense and sorrowful look, until I drain them for her. Again, with a warm, damp paper towel for catching and cleaning. Zo is such a sweet and easy pup.
I do these things when she's standing on the floor and make as little of a production of it as possible. If you don't give Uni a chance to start worrying and fretting, there'll be nothing to it...