22 AWG gauge is plenty big enough for this application.
You would need a bigger wire size for higher current applications, not for LEDs.
Depending on the LEDs/types, typical current draw need is only 10-30 mA (e.g. 0.01 to 0.03A).
If you wire them in series the current across all will be the same, still 10-30mA.
Do not forget to add a dropping resistor in series, to limit the current flow through them.
An example how to calculate the resistor value and power dissipation for this application:
For LEDs having a forward voltage drop of 2.5V, for 20mA current, say 5 LEDs in series, at 18V supply:
R = V/I
R= (18-(5*2.5))/0.02
R= 5.5/0.02 = 275 ohms.
Power dissipated in the resistor:
P=V*V/R
P= 5.5*5.5/270 = 0.11W
So you would be OK with a 270 ohms, 1/4 or 1/2W resistor.
- Sylvain.