It’ll be difficult to do anything without QuickTime installed. The regular (and simplest) way to do it is to use
TMPGEnc along with the
QuickTime plugin for it, but I doubt it would work without
QuickTime (or possibly
QuickTime Alternative) installed. For playback only you can at least try
VideoLan. I don’t believe it requires as high privileges for installation as QuickTime (I don’t think you have to be an admin to install it - I could be wrong though)