Nathan,
Just don't grab the "BIG RED WIRE" attached to the tube, and you'll be fine. In fact, most modern arcade monitors seem to be self-discharging, so hopefully there's very little risk of a high-voltage zap when it's turned off.
Once you've gotten it installed in a cab, there's no problem at all, and until then, just handle it by the frame.
You think you're in over your head? I had to do a board swap on my D9200 (my first arcade monitor), which required me to remove the dreaded "BIG RED WIRE" from the tube...I followed all the steps I could find, used a screwdriver wired up to a ground, and discovered that the D9200 has an autodischarge circuit. No "POW" no "ZAP", nothing...almost anti-climatic (but in a good way

)
Kevin