I'm going to step back for a moment and re-think my original ring-as-conductor bit.
IF I were to assume gold as the conductor (and I safely can), I can determine the conductivity and be very, very careful to limit the current to the levels that I won't have to worry about corrosion, at least unless the ring is left there for months. If I were to pull the current down into the 10mA range, AND send pulses every second or so, it would have VERY little chance of being an issue.
That has me back to:
Round base. Arduino inside to send / receive pulses. Perhaps some more fun electronics inside for any gimmick I come up with. Hollow pole with wires run up for LED. Since the current necessary to run the LED isn't going through the ring itself, it shouldn't cause the corrosion.
At the bottom of the pole are two pads. Split washers would do it. Heck, conductive fabric wrapped AROUND split washers (for a soft landing) would do the trick.
Any objections?