> Do I need to discharge the monitor to change the jumpers or is that area "safe"?
Most newer monitors will bleed off a charge themselves if unplugged for a few minutes. Even with that said, you should be safe with the unit powered off if you stay away from the big red wire. Keep one hand behind your back and you'll be fine.
(even in a worse case, if the monitor is unplugged the jolt from any shock you'd get would only last a split second. I'd be more worried about your hand jumping up into the neck of the tube than I would about the shock itself.)