Cheap way to power blue LED on coin cell
Connect the led to the coin cell. Nothing simpler than that. The high Equivilant Series resistance of the coin cell, as well as a lower voltage than the nominal 3.3-3.6V @ 20 ma, means that it's self regulating.



This is how led throwies work, and any super cheap single coin cell led "flashlight" works, with some plastic to bend the led pins onto the coin cell.

The physics behind it is that leds are like any other diode. They have a current/voltage curve that goes quickly up, so they have a small range of voltages where they are both visible and not dying. A typical blue led will be visible from a few hundred microamps/fractions of a million (pin point light) to 50 milliamps  (bright pop of light as it explodes). This translates to a voltage below it's nominal to a voltage above it's nominal, maybe 2 volts of a difference. And it's nominal voltage at a given current varies. Two of the same brand leds could have 3.35V at 20mA while the other 3.43V at 20mA. And heat etc. The nominal forward voltage is an average and not required to light it. You can do it at a much lower current/voltage.