If in fact your revolver was made in the 1950's it should be fine with smokeless powder. If it is made before 1900 it is probably not. It looks to be in very good shape, could it have been refinished at some point? My 32 looks like yours, except the hammer and trigger and trigger guard are not nickel plated like yours. Plus, the nickel plate on the side of the barrel close to the cylinder is flaked off pretty bad, I think from shooting black powder in it years ago and not cleaned up well. Yours looks to be in very nice condition and where I live would probably bring between $125 and $175.
I am not sure that I would trust that gunsmith; I believe that a revolver manufactured in the 1950's would have the caiber rollmarked on the barrel. I know a lot of the older guns didn't, it was just assumed what the chambering was.
I have three; an H&R 32S&W (I don't have a pic), and two 38s.
Empire State Arms 38S&W
Iver Johnson Safety Automatic 38S&W