Alternatively, one could run a VM with the monitoring software, and have a separate window with notes. As long as the mirror is angled so to hide a small portion of the screen that should be good enough.
To build on your physical solution using polarization: that's easier. You can apply a polarized filter to the webcam (you can get one from an old pair of 3d glasses) and then have the notes on a secondary screen that will then look completely dark on webcam. Maybe lay the device on a black background so it's not obvious that there's a "turned off" device and you're done.
This is all a fun thought experiment. I don't have invasive professors, thankfully. They simply made all tests open book and raised the difficulty of the questions accordingly. That being said, I enjoy trying to work arounf hypothetical limitations...
Yellow highlighters' coloring is called 'Solvent Green 7' and has a peak at about 494nm.
You can buy filters for lenses that will knock out certain bandwidths of light and keep the rest coming into the camera. These are called notch filters, as they take a notch out of the light.
There just so happens to be a notch filter that should know out the yellow highlighter color. Meaning that the light reflected from a yellow highlighter will not enter into the camera.
https://www.thorlabs.com/thorproduct.cfm?partnumber=NF488-15
They are not cheap though, and as such, I've not tried this at home to see how well it works.
Other solutions may exist at to the ideas that these people may have about how your webcam is working. I'd experiment with other lenses, polarized filters, exposure times, etc.
That said, studying is a lot easier than trying to jerry-rig your webcams.