Cygwin is an amazing POSIX based development environment which offers unix like environment with shared library options
But, when you try to install, it will ask for administrative privileges
This article helps command line based argument to install Cygwin without admin right
Type this below command to install Cygwin without admin rights
C:\cygwin64\install>setup-x86_64.exe --no-admin --download --no-desktop --no-shortcuts --verbose --root=c:\cygwin64
Assuming setup-x86_64.exe downloaded to c:\cygwin64\install the above command line argument --no-admin allows the setup initiate without Admin privileges.
Cygwin download location - https://cygwin.com/install.html