All,
I have posted an cygwin installer script that install cygwin following the directory structure recommended by PortableApps.com. Please test it out and let me know your feedback. Installer can be downloaded from https://cygwin-portable.sourceforge.io/.
Download the file cygwin-portable-setup.cmd to PortableApps\CygwinPortable, edit it in case you want to install additional packages and execute the script either in cmd terminal or by double clicking on it. It adds 4 menu items - Terminal, XServer, Automatic Update, Manual Update to PortableApps launcher. Check out the Help contents for more information.
The application is installed in App/cygwin, launcher in App/AppInfo and the home directory for the cygwin user is Data/. X and apt-cyg installation is optional and enabled by default.
I'd like to thank you.
I have updated the installer script. Would appreciate feedback on the installer and also whether it would be possible to make it an official portable app.