That is a great story, gamine!
Somehow, I think "The Hippopotamus Song"--especially the chorus of "Mud, mud, glorious mud, ... etc." would be very 'shower-friendly.'
Then there's also the old song that Looney Tunes characters (Bugs, Porky, etc.) used to sing:
"Singin' in the bathtub [shower], la ti da ti da...".