You ought to be able to use yttria-stabilized zirconia, magnesia, carborundum, or graphite as a cathode for electrochemical machining of metals in a molten-salt electrolyte. I think zirconia needs to be heated up to 500 degrees, maybe 800 degrees, before it becomes conductive, but carborundum and graphite do not.
Magnesia was what Nernst used in his original lamp, with a platinum preheating filament, but it is fragile and presumably requires even higher temperatures to become conductive than zirconia; the temperature for magnesia was originally claimed to be over 3000°, though magnesia melts at only 2852°. Hartman solved the mystery in 01906, finding temperatures from 1780°-2360°, but these were the temperatures at which the globars were operated to provide light, not the lowest temperatures required to make them conductive.
The commercially sold Nernst lamps used platinum filaments heated to redness to preheat the “glowers”, which were presumably already zirconia rather than magnesia, though the 01903 manual doesn’t say, only that they are “porcelain-like”. Hartman said the glowers he tested in 01906 were magnesia. Mills’s history of the lamp said magnesia required “above a red heat”, and explained that it required a ballast resistor to stabilize it because of its negative temperature coefficient of resistance. Nernst used a red-hot iron wire in a hydrogen envelope for this resistor.
Mills also mentions that early carborundum was insufficiently conductive for use as globars.
Another promising oxide for this sort of thing is bismuth trioxide, which is significantly conductive down to room temperature. The monoclinic room-temperature form is four orders of magnitude less conductive than the delta form that’s favored above 727°; analogous to YSZ, doping with other metal oxides can stabilize these more conductive forms to lower temperatures. However, its melting point is only 817°, so while it might be useful for molten-salt electrochemistry, it wouldn’t work well as a globar. (It’s also nontoxic, insoluble in water (though attacked by CO2 unless stabilized with silicate), and has an astounding density of 8.9 g/cc; sillenite, a bismuth silicate, is even denser at 9.2 g/cc, and though very soft, it might be an interesting aggregate to add to pottery to increase its density.)
ECM at the higher temperatures enabled by molten salts ought to permit faster material removal than in aqueous solutions, and might be particularly appealing for metals that are difficult to machine electrochemically in aqueous solutions; however, I think only gold and some of the platinum-group metals really suffer from this.