As for your actual feedback: there is no way to achieve this from the extension. The extension doesn't know where the companion executable is - it is the browser that connects the two applications.
However, you can enable debugging, then you can open the companion log file, which will contain the path to the executable.
Out of curiosity, why do you need to know the location? What were you trying to change in the registry? Is this the reason you uninstalled it? Maybe I can help.