A file isn't that bad of an idea. The file is more hard then the SS is. It isn't going to leave behind much if anything to really worry about. Your not going to weld or heat up this area. A carbide would be a better choice, but not really the tool for the job. Plus, if you follow up with some sand paper for a final dressing on the edge...you should be good to go.
I like to use a flapper wheel. I have a couple different grits just for my SS. In this case, yes. Don't use a flapper on your SS that has been used on mild steel. I like a 120 grit flapper for the final pass.