Powering a 5v Arduino with 3.3v and using a resistor network for voltage droping

I agree onto using a normal diode to drop ~0.7V without energy consumption (or, better, no appreciable energy drawn).

To measure the voltage at the output you need to put something between the diode and GND, like a 220R resistor, then measure the voltage between the diode output and ground: that is what your nRF24 will get.
I'm powering my mini with 4AAA cells and using two diodes in series to drop the voltage before it reaches the nRF24 board: so at no blue smoke.