As always, keep your mind and thoughts together. If you do, you'll be fine, even in the shower. I did read that one should not touch (or even look at) ones Bris. Regarding washing, you can rely on the waters that run down to provide an adequate washing.
Don't concern yourself about the cleanliness. It takes care of itself, as mentioned above. Just keep your mind and thoughts together.
One more thing. Being that it is prohibited to think on holy matters in the bathroom (though I have heard it is permitted in cases of saving a life, which this may qualify for; check with a Rov), what I often do is think on a great, beautiful garden. Something really, really nice. Really, really peaceful. This gets me through when thoughts go south (figuratively and literally, whew).