I would not perform surgury on line cords to install switches. I'd look at solving the more general problem of switched power at your desk. This probably won't be up to code, so don't let anyone official see this, and hiding it a bit is probably a good idea. You can mount a regular wall switch somewhere on the side of your desk in a metal electrical box. Get a line cord with wire ends or cut the female end off a extension cord and have that go into your switch. Coming out of that you have switched power which can go to a bunch of regular wall outlets mounted in more metal electrical boxes under or at the back of your desk. Now you can plug in whatever you want switched to these outlets without having to modify the equipment at all. When you upgrade equipment, just plug in the new stuff without having to modify it.
Having general switchable outlets attached to you desk could be useful for various things. Here in the office I have several switched outlet strips stuck to backsides and undersides of various desks. They come in quite handy. There are a lot of things you need to plug in when you work with electronics and computers.
Added:
As Photon pointed out, I should have mentioned that all these electric boxes should be grounded. That's why I said to make them metal. I meant to say to ground them but somehow forgot.
There will be three wires that come from the line cord that goes into the first box with the switch: Hot, neutral, and ground. Here in the US these are usually color coded black, white, and green, respectively, but don't rely on that. The neutrals of everything coming into and going out of a box should simply be connected. The ground should also be connected, but also to the box. There is usually a separate screw inside the box just for clamping a ground wire to it. The hot line is what gets switched in the first box. What comes out of that box therefore is the same neutral and ground that went in, but the hot is either connected or floating depending on whether the switch is on or off.
If you are paranoid or want to go further, you can use a DPST switch to switch both hot and neutral. Never switch ground. That must always be reliably connected straight thru and to every metal box.
If you're really paranoid, you can install a ground fault interruptor in the first box immediately to the incoming power. That shuts off the power if it sees a imballance between the hot and neutral currents. When all is working right, all the current that flows out on the hot line should come back on the neutral line. If something goes wrong, like your body is conduting between hot and a metal radiator pipe for example, then the hot and neutral currents won't ballance anymore and it shuts off power before you get too fried, hopefully, if all works right.
I found several USB controlled relay modules, but unlike many others this one does not require a separate power supply; it's powered from the USB bus.
The module uses a virtual COM driver to control the relays from your PC. So any programming language able to talk over UART can be used to control the module.
On the same site you'll find modules with 8 relays as well.
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On my monitor the soft-press button puts the device in a Sleep mode. The screen is off but the power button remains on, just orange rather than green(Powered on)! I noticed that when I press the soft power button again the monitor turns on more quickly then if I pull the power and then restore it. All things considering if your LCD has a back-light being turned off and on would makes me wonder about the stress on it. I'm not sure there's any evidence that turning it off and on in this manor would worsen it. I believe the back-lights are fluorescent bulbs and simply removing the power to theses should present no problem! My thought is go for it!