Bryan Ferry has done loads of covers of show tunes and standards, both as a solo artist and with Roxy Music.
I don’t know if it exactly qualifies as a showtune, but I just had one of my usual streams of consciousness: saw a documentary about Priscilla Presley which contained a snippet of Elvis singing My Way, somehow thought about Sid Vicious’ infamous version and remembered this thread: So here it is in all its glory (I think you can file this under ‘alternative’ per the thread title).