Could I use 40ga Litz wire to power one LED which draws 20mA? A best guess is welcome.
I guess one question is... how long is your wire going to be? It the total current draw 20mA or are there multiple LEDs.
Wire gauge is determined by two things:
1) how much voltage loss can be tolerated.
2) at high currents you have to consider the heat generated in the wire.
If I assume you are powering with 5V and your LED voltage drop at 20ma is 3V. Then you resistor is (5-3)/0.02 = 100 ohms.
In theory you could use a wire that is 100 ohms (very fine and very long) and eliminate the resistor. Or any combination of resistor and wire.
Consider #40 wire (single strand solid) for 10 feet, the resistance is only ~ 10.5 ohms. You could use this wire and a 90.9 ohm resistor in place of the 100 ohm resistor.
Hope this helps.