Yes, exactly. However you should be aware that two separately shielded leads are required for left and right audio to avoid crosstalk between the channels. Thus 3-conductors + shield is not exactly what you will need!
The exakt dimension of the wires doesn´t matter so much IMO. You should use a cable that is suited to be used with LF signals (audio frequency range). The exact wire dimensions are more relevant with high frequency as used by e.g. GBit ethernet cables. Generally speaking a thicker cable will have less impedance and will lead to fewer signal degradation than a thinner cable.
Btw. thanks for clearing the exact meaning of "AWG"!