Although I agree with the consensus opinion here, there is another factor to consider: this is a very low demand part here.
Another reason why, unless it was $100 or so, that its not worth doing, is because the factory marked the barrel assemblies up by the ears where it latches. These old S&Ws had a SN on the barrel, top latch, cylinder, usually the ejector, the frame, and one (right) or both of the grip panels. As a collector myself, I always check numbers, just to be safe. Since yours would obviously mismatch after getting a new barrel, it then becomes a mismatched shooter.
Try calling numrich, jack first, popperts, and try posting a want ad on the S&W forum. Maybe you will luck into something on the forum.
In general, it will be a hard part to find, but since no one wants such a barrel either, you could get lucky.