Yes, caution should be used in handling a monitor, but I almost never discharge them until I get them out of the cabinet. For my part, I find it safer to do when I can get at the second anode (the "suction cup") cleanly. Having said that, I always discharge, even if I am just putting the monitor aside.
I STRONGLY DISAGREE that you should lift the anode cap to check things out prior to discharge -- to my mind that is far more dangerous than removing the monitor without discharging.
I mean, really, why would you want to put your exposed fingers close the one part of the monitor that is dangerous while powered down ?

Discharging is not a big deal, although it can seem pretty scary until you do it a couple of times. I have never had a loud pop and often get no pop at all (so I repeat the process a couple of times, just to be sure).
There is a video in
this thread that is pretty good.
Obvious rules like making sure there is no power to the cab, not licking the anode cap and making certain that nobody can plug in the monitor while you are away from it

apply. Also make sure that you can handle the monitor and get it to where you want without dropping it -- imploding (then exploding) tubes suck!