The warning in that pdf is a very general warning. It's saying this: "If the analog board died because other stuff connected to it misbehaved, then the new board is at risk of similar damage." It's certainly possible for this to be true, just as it's possible for a previously undetected comet to crash into your home. However true, neither is probable enough to constitute a source of concern.

The CRT's charge won't harm you, but it can surprise unpleasantly. A piece of wire will act perfectly fine as a "discharge tool." Assuming that the tube hasn't been removed, connect one end of the wire to the ground lead in the frame above the CRT (see pic in my doc), and stick the under end under the anode cup. That's it.