Yes, you can use Stainless Steel. What type of cable do you have, and what diameter?
I run quite a bit of stainless for otter and live coyote work. The cable I run is a semi-custom cable. It is a 7X7 stainless cable that "began life" as 3/32" diameter, but then was run thru a swaging die, and swaged down to a 5/64" diameter. It is an expensive cable, but the price is well worth it for the work I put it to. I know some Western snaremen who call this cable, "smooth line".
I paint my stainless, at least by mid-summer, for use in the coming season.
I find that if I hang cable for spray painting, the paint tends to run down the cable, and can become a problem when the snare fires. I lay all my cable to be painted on a flat surface, and give it a quick once over. When it has dried completely, I turn it over, and hit the other side.
This method of spraying works well for me. Someone else may have a better touch than I do.