Considerations for transmitting the signal from a MEMS microphone over a short cable?
My opinion only: so long as the output impedance of the preamp is fairly low, you should NOT need to provide shielding between the output of the preamp on the card containing the microphones and the other card containing the ADC.

Several factors affect noise pickup.  

First is the actual level involved.  The higher the desired level sent down the conductor, the less effect external noise has.  It's a matter of ratios.

2) Output impedance of the source determines just how much external noise will affect the signal.  In an ideal world, zero output impedance is immune to external EMI fields.  We don't live in an ideal world but in general, the lower the source impedance, the less effect external EMI has on the signal.