When I've caused this noise at home there weren't any mics around. Just a stereo system left turned on, or computer's speakers left idling. The radio (i.e. a transmitting GSM cell phone, as it searches for a tower) overpowers a nearby amplifier's ability to reject it because the FCC dropped the ball years ago by not ensuring cell manufacturers play nice with normal audio gear.
Newer phones, or perhaps simply phones operating on 3G are better designed. My iPhone4 -- an old phone today -- won't create this noise. Our original iPhone always did ... but it's 2G only. That last part may be important, because if it's caused by the older 2G cell network, even a new smartphone could cause the interference if it automatically switches over at the venue due to poor 3G reception.
Keep in mind, none of this discussion applies to CDMA phones (Verizon, Sprint networks.)
I really doubt it's normal "RF noise" that you could reject with batter cabling, because I do not suspect your mic and cables are picking it up. I think your preamp or other circuitry is, honestly, and that only greater distance away will cure it.
Try the new cable, but unless you can create the same conditions you won't know if it actually helps.