Cygwin officially gives a vague answer about where there is a command-line installer for it or not. A quick search gave two options: cyg-apt (last updated in 2009) and apt-cyg (currently maintained). I’d try apt-cyg.
lynx -source rawgit.com/transcode-open/apt-cyg/master/apt-cyg > apt-cyg install apt-cyg /bin
And you are all set.
If you do not have wget, install it.
apt-cyg install wget