There is no "slim-version".
There is a Slim Installer, but that's the installer not the CCleaner programme - It installs exactly the same CCleaner.
As for blocking connections:
TBH I don't understand why people who deliberately disable/block/cripple parts of an app then expect that it should still work as intended?
If you deliberately stop something from working as designed then it's your own fault when it won't work properly.
Would you block your cars cooling system (put a nos