[morzh]

The second cap probably won't eliminate the hum: it occurs due to the ripple current in the field coil used as the filter coil (if it is not then there is usually no humbucking coil in the speaker either) and there is always the ripple current through the field if used in the filter.
However making the humbucker is easy - put a few turns of wire around the field coil and connect in series with the voice coil. And if it makes it worse - reverse the polarity of the humbucker.
Folks here probably could tell you how many turns it needs to be. Regular PVC insulated wire will do.