his must be the third or fourth time I've posted this. In the world of irons (yes stainless steel is an iron), if it will harden; it has all the properties of ordinary steel. Including magnetic properties. Plus it will rust.
Your better off leaving the barrel alone, as there's nothing your going to run down the barrel that's ferritic. Sometimes heat will change the granular structure enough, but will also ruin the barrel. There's another way using a D cell battery, but have never done it. Best way is to run the barrel thru a demag once or twice. No more than that, as you'll probably magnetize the whole barrel.
gary