Larry Hall kindly advised:
Assuming you start bash now by clicking on the icon for cygwin.bat,
simply
edit that file, and replace "bash" with "zsh". You'll need to review the
man page for zsh to see what are the appropriate flags to pass to get a
login shell. I don't have zsh installed otherwise I might give you a
clue. ;-)
Are you kidding? That was the best clue you could have given!
My mental model was wrong. I was looking inside the system for
something that was in a "DOS" batch file.
Now all that's needed is a way to let us not install bash... Why does
setup.exe insist on selecting the bash package? I have to remember to
cycle it back to "Skip" every time.