Welcome to the forums from the Wiregrass! It appears to be a .32 Hand Ejector, Model 1903, 1st Change from 1904-06. Yes, it is smokeless. The grips are post WWII. It would originally have had black hard rubber grips.
Thanks for the quick answer. I was having no luck finding any information on this gun. Are parts available for these? I think the hand needs replacement. Lock up is fairly loose DA and in single action it is nonexistent.
Parts are problematic as the action on these guns went obsolete around 1905. You may have to find a gunsmith or machinist to fabricate parts. I have to say that the condition of that gun is poor and it would probably be worth more as a parts gun than to spend money on it to make it functional.
Poor is a kind word. . This gun is in terrible shape finish wise. The DA lockup isn't much worse than in my pre 1900 s&w's which I use to shoot the pocket pistol side matches in cowboy action. The gun was in a batch of guns I bought because I wanted a couple that were in the lot. If I could find a hand I would fit it myself. Its not worth it to me to put a lot of money into it.
I have another question. The S&W in the picture is one that I use in the side matches. I assumed that it was pre 1900 but I really don't know. The markings on the top of the barrel state Smith & Wesson Springfield Mass U.S. Pat and a bunch of patent dates including "reissue July 25 71 May 11 80 Jan 3 82