I too have a REL sub, but no hiss or hum problems. The REL-supplied high level cable is not shielded, but this should not be a problem since speaker level voltages are going down it, and these should not be susceptible to RFI.
Does the hiss / hum go away when the REL is switched off ? How about when the REL is disconnected ? Do both go away or just the hum ? Is the hiss / hum the same regardless of which source you select ? What if you switch all your equipment off one by one ... does the hum or hiss go away at any point ? How about disconnecting major appliances around the house (maybe even isolate by switching off breakers one by one)? These are the steps I'd go through.
Hum is usually a power supply problem (e.g. earth loop). Hiss : I'm not sure : could be any number of reasons. Some amps are quieter than others, some are more / less susceptible to RFI. Shielding is much more important on interconnects than speaker level cables.
So long as both are well below the normal listening level of your music (as I assume they are or it would be more than a minor problem) I can't see why it would cause any problems with the speakers, but I'm no expert in these matters.