It's been a looooong time since I've tried anything like this, and you'll have to research the steps to be sure, but something along these lines may allow differing versions of Java to coexist like you want:
- Install the older version as default. (IE should access this fine.)
- Download the newer version in the SDK+JRE form; install/unzip to your choice of location.
- Setup batch scripts that will change your Java-related environment variables from the older version to the new version temporarily (ie, from one particular shell).
- Setup another batch script to call the first, setting up the environment for new Java, and then startup Firefox.
- Make a shortcut on your desktop that runs that script instead of starting Firefox directly.
Of course, there may be an Easier Way(tm), but that's what occurs off the top of my head.