I believe this at least used to be feasible to a limited extent with earlier versions of Java - I don't know if it still is.
Most of the registry entries are used for things like browser plugins, as you mentioned in the question. If you just want to be able to run Java (e.g. from a batch file), that's one thing - but really installing it is a different matter. Even if you're just wanting to run it, you'll need to be careful to always explicitly use the one you intend, rather than using the installed one accidentally for part of your application.
What's your actual use case? Do you actually need a browser plugin? What aspect of the configuration are you interested in? A lot of the control panel configuration is to do with updates and browser integration. Many other aspects can be controlled using command line options to set specific system properties.