Thousands of packages.. Creating a static dump of them will be outdated in day. I know what you mean.. But the best bet is to do the effort once, keep them updated and backup before deleting again.
Cygwin installation guide says,
By default, setup.exe will install only the packages in the Base
category and their dependencies, resulting in a minimal Cygwin
installation. However, this will not include many commonly used tools
such as gcc (which you will find in the Devel category). Since
setup.exe automatically selects dependencies, be careful not to
unselect any required packages. In particular, everything in the Base
category is required.
So, if you know which packages you need, its not much of a trouble, because the most important ones will be installed by default. You can always install any package you want after you've installed Cygwin. There is no need to install them all at once go.