I'm not sure what you mean by "REW doesn't allow it". If the system has an audio input you should be able to access it in REW. REW doesn't care how many input channels there are.
Excuse me for ambiguity. I mean measuring impedance (for calculating T/S parameters). This mode uses a resistor that is connected to two inputs to measure the voltage drop across it (which means the current in the circuit).
By phrase «add this “mono mode” into sound card setting» I mean allow REW to use only one input signal (because it will be produced by differential amplifier build on OpAmp — it will be exactly the same what now is doing by software algorithm which calculates difference between one input channel and another).
P.S. sorry, English is not my native language