It doesn’t matter if you used the convenience for number one or number two. You are expected to wash and dry your hands afterwards.
The obvious reason for this is that there are so many germs in the toilet and of course, because it is the basic hygienic thing to do. Imagine using those dirty toilet hands to touch food or touching your eyes, nose or mouth. The rule is; always wash your hands after using the toilet.
But then you cannot leave the place with your hands wet. And this is where hair dryers come into the picture.