I don't know much about CRT repair but you being able to find exactly what one piece (capacitor etc) is causing the problem will not be likley. If anything you will have to order full boards to replace. I had a noisy View Sonic and on there website was actually a spot to order specific parts and even a service manual.
Not sure about the de-charging it. I know it can contain more than enough to kill you but I think that really only applies when it is on. I would just get a screw driver with a rubber handle and make contact between the + and - on all the caps.