Yes. The red core will be the signal, the braid around it will be ground.
The closer the braid is (you will also see it woven around the core) the better the shielding.
Could you try to shield the preamp itself?
The best would me a metal enclosure.
For a test you could do the following:
You could wrap some clingwrap (plastic foil) around it (for isolation) and then aluminium foil around that package.
The output cable should also be shielded.
The signal level in that cable is higher, so the influence will be less.
It would likely also help to make the connection between the mic and preamp shorter.
Between the preamp and computer will become longer that way, with a higher signal level.
Both sides will be with the shielded cable.