When I used to tinker with CRTs, for better or for worse I made the long screwdriver, wire alligator clip device described above. It worked well and I always had a gloved hand with my other hand behind my back. I was using disposable tvs from thrift shops so I didn't mid if one or two broke. On tvs that were recently plugged in there would be an arc and a pop. On many of the older set that sat around for awhile there wouldn't be any discharge. I would then keep trying to make sure before I removed the suction cup.2) I also read that it is not recommended to use a screwdriver to discharge?!
Also, make sure the set isn't plugged into the mains when the cover is off. It is easy to forget and accidentally touch something you shouldn't.