most modern flybacks (since pretty much the 80's) have a resistor network in them that bleeds off excess voltage.
unless your unit is old (pre 80's), the tube especially large (27, 30, 33"), or the flyback is damaged or compromised...
leaving the unit off for a few hours is often enough to get rid of the buildup in the tube.
yes, i said tube. It's not the electronics you have to worry about, it's the tube. it's construction is similar to a capacitor... a very high voltage, low capacity capacitor. google up yourself a set of plans to build a Leyden jar, then take a look at how a tube is constructed, they have more in common then you would think.
in closing, no. i don't know where you put your keys... oh right, no, you won't get zapped. but as an extra precaution, before you place the anode cap back on the bellybutton, hook up your discharge rig and touch the bellybutton to discharge it again, sometimes the charge starts to leak out of the glass and the tube builds up a bit of a charge again. then go ahead and snap the cup back on again.
Pro tip: turn the suction cup inside out and use it as a handle to clip the legs of the clip into the bellybutton.