Okay, thanks for the information guys. I'm sure the pot itself isn't high voltage, but the flyback definitely is and I'll need to discharge it. I watched some videos last night about soldering through-hole PCBs and discharging the flyback and I'm pretty confident I can handle both tasks. With regards to the "pincushion" adjustment, I didn't see anything like that in the manual. The remote control board has R / G / B / Brightness, and then horizontal size and hold, vertical size and hold, and a couple of other pots (I think the 4 color/brightness and 6 other pots) and tweaking them didn't affect the bulge as far as I noticed. On the chassis itself there was some sort of vertical pot and some sort of horizontal pot, as well as 4 others that I don't think had anything to do with it. Regardless, I don't want to tweak them, as I'm pretty sure they'd just break off like this one did... Maybe I should replace them all in one fell swoop.
Some questions I haven't found answers to in my searches yet:
1) What's with the neck board? Does it just pull off and then push back on? Do I need to adjust stuff (the rings on the yoke, etc) if I remove the neck board?
2) Should I remove the entire monitor (frame, tube and all) from the cabinet, or should I just discharge the monitor, detach the chassis to work on, and leave the rest in place? I'm hoping the latter is ok, although the videos I've seen have the entire monitor assembly removed from the cab...
3) How can I tell what kind of replacement potentiometer I need? I don't have a multimeter, but would be willing to pick one up if it's what I need to do the job. I have the manual for the cab, but it doesn't seem to get so in-depth as to the actual circuitry of the chassis... And no, at this point, I'm not sure which chassis I have, and probably won't be able to tell until I get it disassembled.. there's no obvious stickers or screenprinting that I can see from the back of the cab.
4) I plan on replacing caps as well, as long as I have the chassis out. I can't find a cap kit list online (a task made even harder by the fact that I don't know the exact model of my chassis), but I'm assuming, worst case scenario, I can make a note of all the caps on the board, go to Radio Shack and pay through the nose. Is this correct?
EDITED TO ADD: I've researched and my best guess it's a Nanao MS8-29FN87, visible here:
http://www.zax.com.au/spare_parts/monitor-chassis.html. Googling this model number only returns a result for the site I just linked. :/