I realize this is almost identical to Windows equivalent of the Mac OS X “open” command and Linux equivalent of the Mac OS X "open" command, but I’m asking specifically about a command I can run in the Cygwin shell to use the current Windows UI application bound for the argument’s extension, that as on OS X opens that application if necessary, and opens the specified file in that application.
The cmd.exe start command isn’t an option in the Cygwin shell, nor are xdg-open or gnome-open available through Cygwin.
Is there an equivalent?
You seem to have missed this one:
Open a file from Cygwin