It's simple...twist your ground and shield wires together and connect them to the outer side of the RCA connector. The positive line goes to the center conductor.

Additionally, if you would like to try it, don't connect the shield to ground on one end of the cable.

When using the interconnect, connect the end with the attached shield to your audio source, and attach the end with the detached shield to the equipment that is receiving the signal.

The shielding will still do it's job - being grounded to your audio source - but any EMI/RFI picked up by the shield will not be passed on along with the audio signal. Additionally, there will be no ground connection between the units, eliminating this potential source of ground loop hum.

This is the primary reason some interconnect cables have direction arrows on them. It isn't that the wire is magical and only works in one direction, rather this design only works correctly when the interconnect is connected properly.

Thanks Mike53 and Elk. The cable in question has 3 solid cores. One with transparent shielding, the other 2, blue. So, I assume that the transparent one could be taken as the signal conductor, while the 2 blue ones could be twisted together as the "shielding" conductor. I've not come across the way interconnects are connected as suggested by Elk. I certainly will try to see how it works.

Elk is correct...you only need to use one wire for ground.
Yes, use the transparent conductor for the signal. As for the 2 blue wires, look close to see if one has a faint white (or other color) stripe or dots...so you can identify one blue wire from the other. If not use an ohm meter to do so. If you don't have the same blue wire grounded at each end you will get noise on the line.

I guess I have to further clarify on the ground connection. Is it that only for cables with direction arrows grounding should only be connected at the audio source, not the receiving end, while for cables without these direction arrows, grounding can be connected at both ends of the interconnect?

The type of cable does not matter. You can either wrap the two blue wires together on both ends, or you can leave the shield detached on one end with either type of cable. The arrow just reminds you that the end the arrow points to has the lifted shield wire and that this is the direction the audio signal is going. The arrow is just cosmetic.