The way I've dealt with this at the gym is I bring a bag with me to the shower. In it is my shampoo, etc, a fresh diaper, and a suction hook. I added this several years ago because the hooks outside the showers are frequently already taken. The hook allows me to hang my bag inside the shower high enough to keep it dry. After the shower, the fresh diaper comes out, gets put on in private and everything else goes back into the bag. I wrap my towel around me and head to the locker to finish getting dressed. It's become an easy routine for me that I hardly give a second thought.