Take the monitor out, the cabinet will be way easier to deal with if it is out.
Don't let people mislead you into reading a huge monitor FAQ, if all you are doing is removing the monitor in one piece. All you need to do is remove the signal cable, unhook the power cable, and unscrew or unclip the green earth ground (if it is even there), unbolt the monitor and pull it out.
When simply removing or installing a monitor the ONLY safety bit you need to remember is "don't pull the suction cup off the tube". As long as you don't do that then you aren't going to make the monitor explode, nor are you going to fry yourself.
You DO NOT AND SHOULD NOT be discharging a monitor just to remove it from the cabinet. Doing so adds an element of risk to an activity that previously had none and serves no purpose.
Removing monitors isn't a big deal, I rarely go a week without pulling one.