Stainless steel should be OK as long as there is no electrolysis taking place. For that keep voltage as low as possible (0.5 V will do) and - if possible - use alternate current for the measurements. Plus, you don't have to keep it on all the time, measuring resistance once each 10 seconds (or half a minute) should do.
And yes, low current is a good idea, but currents in electrochemistry are not exactly ohmic.