If "just" requires ordering specific electronic components and soldering, it's not "just" for most people.

Also not the easy kind of 1990's LED soldering, like tiny surface mount soldering.

I suppose that really depends on how hard they’re trying to prevent you from doing that…

* They could measure the forward voltage of the LED when driven by a known current. Bonus points for measuring at multiple currents. Remember that the forward voltage depends on color.

* They could measure the reverse leakage current at a known voltage, and compare that to the illumination from the camera’s exposure feedback. Remember that every LED is also a photodiode.

* They could vary the LED driver current to heat it up, then measure that both of the above measurements are compatible with the higher temperature. Remember that most semiconductor properties have a strong temperature dependence.

So it would be pretty easy to detect most simple mods if they really wanted to.

You could replace the led with an IR led. That should have mostly the same electrical characteristics of an LED but emit no visible light