Thanks, and yes, that makes sense that you are using the 851C to control the volume.
As far as cables, you should use the same pair of normal interconnects for both connections. This should give you a good full range signal into the sub, then that same signal out to the amp, less the low frequencies due to the high pass filter.
It wouldn't surprise me that the only difference in some subwoofer cables is labeling and being sold as a single instead of a pair. Even if there is a difference, you still need to use normal interconnects.