The gauge is not as critical as the length, as long as the insulation is single layer and not sheilded you will be fine, and yes 1mm will make a differance but not a fatal one.
However the previous post is not correct in saying that a longer antenna will do no harm.
If the 2.4G was a RX only this would be true but the 2.4G RX is also a TX in that is how it talks to the TX to bind each time you turn it on. The frequency is the total size of the radio wave IE a 2 meter band radio uses a wave that is 2 meters tall. Yes radio waves are that big. A radio antenna is an exact fraction of the wave height, if it is changed the recieve and transmit capability of the radio will be lessened, to short or long will cause problems in the transmit circuts, overheating them and frying the IC.
Hope all this helps understand why the antenna length is critical.

Ron Sr