Gents,
"Noise" from the Hard Drive may come from several sources like vibration (possible), electro - magnetic (I doubt it), and power source (more likely) if it actually is impacing the sound transmitted by this small speaker system.
By removing the speakers from the case, while keeping them connected, you can eliminate vibration from anything in the case (HD included); and if the cables are long enough to go a few inches outside the case, any direct electro - magnetic noise should also diminish.
If you shield the cables (wrap them in a single piece of tin foil for their whole length for test purposes => and ground one point to the metal case) then almost all induced electro magnetic noise should be gone as well.
If the noise is power supply related then things get much tougher.