How can I safely carry out an electrolytic etch on stainless steel without producing relatively harmful by-products?
Sand or shot blast it instead.  Rub it with crushed aluminum foil and saltwater.

Everything is harmful.  Voltage determines products.  Use the minimum voltage (slow way to travel).  Don't use a chloride electrolyte.  (TEST FIRST!) Use hydroxide, carbonate, (nitrate - Homeland Severity and OSHA will beat on you), sulfate, electrolyte (note solubility of metallic byproducts after reaction with electrolyte).  The larger the charge on the ion, the slower the kinetics.  Vent the chlorine plus inert air through lye solution to make bleach, or through a solution of reducing agent.

Cr(III) is OK, Cr(VI) is a carcinogen. Reduce spent electrolyte with sulfite, Vitamin C, zinc granules, FeCl2, shredded scrap iron, steel wool, etc - and have a way to test for Cr(VI) residual.  

Before you vent or sewer anything, talk with your Safety Officer.  The EPA and OSHA are carnivorous.  it's always a good idea to be a good upstream neighbor.