I've never really understood the desire to use the button on the display to turn off monitors - does allowing the monitors to be switched off by the OS not solve basically the same problem ?
I used to turn them off with the button on the monitor (when all my monitors were DVI), so if the mouse was moved by accident during the night it wouldn't wake the monitors up. Right now I have to let it go to sleep normally, and then hope there isn't some strange vibration that is big enough to trigger a wake.
Edit: Better language and more info.
Edit: Oh, you're talking about things waking your computer up? Maybe turn off 'wake on USB'? Although that's less convenient otherwise. I know when my desktop computer is fully hibernated, mouse motions don't wake it but button presses do. And you can get into this state (assuming Windows 8+) by right clicking on the Windows icon / 'start' button and selecting 'sleep'.
Essentially this is a convenience thing, it used to work perfectly fine, then they added HDCP to make things less convenient.
Like I said, I'd be fine if the software (well Windows in my case) has a switch to disable HDCP and restore the old functionality of always assuming there's a monitor there.
I can dig it up for you if you want it when I get home.
EDIT: Upon re-read this doesn't really solve your accidental wake up problem. Oops.
Right now, my monitor is in my bedroom. If I let the OS shut off the monitor, it still shows a little white pulsing light to show it's in sleep mode. That's really annoying when I'm trying to sleep.