Some very early Airweights were made with non-magnetic alloy cylinders. These guns are quite rare and it's very unlikely that you have one, but if you do, DO NOT FIRE IT. The alloy cylinder is too weak to withstand anything but light target loads, which is why S&W stopped using them after only a couple of years. FWIW these guns are valuable collector's items. If you somehow stumbled across one, you should be able to sell it and buy several other guns, or maybe a gun and a nice vacation.
Also, do not send such a gun back to S&W for repair, refinishing, or anything else. From what I've heard, a alloy-cylinder gun will return from S&W with a steel cylinder thus ruining the collector value.
Smith, and Wesson, and Me. -H. Callahan
Well waddaya know, one buwwet weft! -E. Fudd
All bad precedents begin as justifiable measures. -J. Caesar