I didn't change to a grounded cord. I always use an isolation transformer on the set I'm working on but plug the SG right into the "raw" line. You don't always have to clip the SG shield lead to the set chassis, or if you need to, it can be through a cap. Most of the time just laying the output cable from the SG near the radio or near the IF tube when setting IF is enough, so SG-to-set grounding issues are under control. And I haven't used my SG in the shower, yet!
