I have a shower packer plus harness that I used when my bottom dysphoria was really getting to me, but I've managed to get to a state where I don't use it anymore. During the time that I was using it, I still had to wash down there, but at least I felt better about having the right kind of dangly bits--sort of, since the packer wasn't perfectly formed. Still, someone suggested it above, and I can say that I found myself much more comfortable in the shower. It's worth a try.
I've never blown off a shower because of my top half. A regular binder is pretty big, even the small ones. But people have used waist slimmers, the kind you buy at Wal-Mart, for binding purposes; they tend to be about eight or ten inches wide, so they are smaller and simpler than a full-size binder and might be more convenient for showering. Still, I don't know how a guy can get clean if he wears a binder in the shower. After all, you have to wash all around there, as well as underneath if you have any droop at all.