A chromium-free welding consumable and a method of welding stainless steel to reduce the presence of chromium emissions. The consumable is made from an alloy that reduces the emission of chromium during a welding process, and include predominantly nickel, with between approximately five and ten weight percent copper, up to approximately two percent by weight of ruthenium and up to five percent non-copper alloying ingredients. Welding consumables made from the alloy are particularly well-suited for welding austenitic stainless steels, such as type 304 stainless steel. The method involves using chromium-free weld filler material with a stainless steel base material.