Are you SURE it's the wire and not the endpin rod or thumbscrew? Engel endpin assemblies are notorious for rattles.
If it is indeed the wire, and it's stock (rigid wire with two cap nuts on the front of the tailpiece), remove it and promptly discard. Replace with a braided aircraft cable or similar. This will also generally squeeze a little more sound from the bass, and you'll have the peace of mind of knowing the cable won't eventually fatigue and possibly break like the solid "coat hangers" can.
Hell, if you're going to go to the trouble of changing the wire at all, consider having your luthier fit a wood plug / cork-lined endpin while you're at it.