If you hold down Ctrl while clicking on a filename or link, or you
select a string and choose 'Open' from the context menu, mintty will
attempt to open it in basically the same way as if you'd passed it to
the 'cygstart' command or you double-clicked it in Explorer. So a
weblink will be opened in your browser, a directory in Explorer,
a .txt file in your editor, and so on, and it can be tweaked using the
usual Windows mechanism for associating file types and protocols with
applications.
Andy