Power consumption / voltage regulation
There is the NCP4680x regulator. It comes in a tiny 0.8mm x 0.8mm footprint: -



Downside with any regulator is that it needs input and output capacitors but you might be able to mount them on top or have something closeby that will do the job. This version has an absolute max input voltage of 6V but it was just about the first hit when I googled "smallest voltage regulator".

Output voltages available in 0.1V steps from 0.8 volts to 3.6 volts and it can supply 150mA but watch the thermal situation because it has a thermal resistance of 350degC/watt. I'd recommend a dropper resistor with this device to both reduce power heating of the chip AND drop voltage to maybe 5V under minimum load conditions.