Need to identify wires coming from external AC Unit
Connect one to Y and the other to C -- it actually doesn't matter which one is which

On an ordinary air conditioner like yours, the Y and C wires going off to the outdoor unit connect directly to the coil of the compressor contactor (basically, a big switch that is turned on and off by an electromagnet).  Since they carry 24VAC to the coil to turn it on when the thermostat calls for cooling, that coil is polarity-insensitive (it has to be to operate on AC, after all).

As a result of this, it does not matter which wire in the air conditioner cable goes to Y and which goes to C, as long as one goes to Y and the other goes to C, and they're both hooked to the contactor coil on the other end.  So, go with your preference, or even flip a coin, when it comes to labeling!