INTP:
I don't think a break beam is even necessary. Put both components on the same side and let the hand reflect. Same as on all those LED coffee tables. The simple modules I've built that were purely analog in design, only required a handful of components. With an MCU, an IR LED and an IR photodiode with a few resistors and you'll have a very rudimentary proximity sensor perfectly suitable for your project that will be easier to hide if you put them next to each other and use reflection instead of break-beam config.
That would be a good option then! The only disadvantage I see is that it would require to make two small holes in the housing to let the emmiter and reciever work. Or maybe we find even a better way of hidding it.
wvmarle:
A ring wire through your lamp (you say it's a circular one) may work really well for capacitive sensor. They can be made really sensitive (look at how a theremin works). Least bulky for sure, but stands and falls with proper grounding.
Well Its acctually almost an O, its open("cutted") at the top. A curvy "U" would be a better description. Could your idea work anyhow?
Reference image, without the plastic piece: