Welcome to the Forum. The proper name for this model is simply 38 Perfected, not 38 Double Action. I have a few of these and they shoot and function just fine. The 38 S&W that is currently available is made by Remington & Winchester is perfectly fine to shoot in your revolver. All of the examples made in this model are "modern" firearms, introduced in 1909. It is not a common gun to find, but there were almost 60,000 made. It is speculated that they were popular export guns for Europe and South America, which may be why not many are seen in the U.S.
If you are interested, there is more information on this model in the following link.
http://smith-wessonforum.com/blog.php?b=109