Thanks for the pics, that helps a lot. Based on what you have there, I would find it easier to remove the power supply altogether and run new power wires for the monitor. Unless you know for a fact that your monitor does not require an isolation transformer, make sure you use one or you could seriously damage the monitor and yourself.
You will also want a power switch for the monitor, too. Radio Shack or other electronics retailers carry a variety of AC power switches. The easiest one to use for this will be a SPDT switch,
something like this.
If it were my cabinet, I would wire it as shown below. You could also include a line filter, too. Bob Roberts carries everything you need to do this, or you could get everything, except possibly the isolation transformer, from someplace like Radio Shack.