It is possible that the HDMI cable is acting as an aerial (when the blue-ray player is off), picking up the noise. This could to due to the signal outputs floating with the player off and things might not be improved with a better (screened) cable.
One thing to try is unplugging the cable at the player, but leaving it attached at the TV. With many permutations of connects and disconnects, it might be worth writing down the configurations where interference is observed – allowing you to sit back and analyse the result to find a solution.