When I was dealing with potentially dangerous power, I've always used my right hand only and made sure my left hand and arm didn't touch anything.  While I've never been zapped by the CRT (and I've worked on the huge projection TV that can have over 80,000v) I did get zapped by live 110v a few times and once 440v line.  No injuries fortunately other than scared out of my wits.

Still if you're nervous, find someone who knows electronics and CRT, share beer and pizza and let him work on it.