Avoiding ground loops with multiple coax cables
Some approaches come to mind:

1) use two cables of the same length and twist them together.   The goal is to minimize the difference in the dynamic magnetic field exposure between the two coaxes.

2) break the shield at one end of one connector and capacitor couple the shield to the connector.   This well help with DC and low frequency loops. 

3) measure the currents in one of the braids.  If low enough,  accept the noise and get on with your project.