Mute controls across all browser windows launched by the course

I think you have correctly determined that a "global" mute control within SL is neither feasible nor practical. However, taking a cue from a different post about downloading screenshots - perhaps you create a button or marker that advises learners to mute the PC at the system level (a couple of "be sure you do this..." screenshots, maybe) and then at the end - or near the end - reuse that same button or marker but advise them to unmute the system.

That seems both reasonable and would allow you to achieve your desired outcome.