Anyone have any ideas on how best to automatically and en-mass delete all my non-steam game links from my games menu?
I believe that simply deleting the shortcuts file, which is
<steam installation dir>/config/shortcuts.vdf, should do it, but I haven't tried it myself so I suggest backing it up first. I don't believe it should do any harm in any case.
Another surefire way is to remove Steam and re-install it, but even if you back up all the game data locally first and then reload it, the whole process will take longer than just removing all the links one by one.