I don't see any harm in trying, given that I've managed to get SDK operations working without the main Android Studio UI. Temporarily rename the SDK directory to keep the uninstaller away, then uninstall Android Studio, then rename the SDK directory back.
If you do this, make sure you know how to use the command line for sdkmanager.bat, just in case your SDK needs new libraries for future updates to GMS 2. The official installation instructions will likely keep using Android Studio, so you have to be self-sufficient in that aspect and know how to act.