Welcome to the Forum. Stocks were optional target style and if ordered with that set, they would have been the only set sent out with the gun. When the company sent a revolver out with target stocks they would have moved the serial number to the front strap as you noted. If it was sent with a standard set, the stocks would have been standard hard rubber round top service stocks with the serial number on the butt.
Many combination sets have been put together over the years, so you should check the single shot barrel over closely for a serial number. Also, look at the underside of the latch for a number as well. Let us know what you find. Also, check the serial numbers on the rear of the cylinder, the underside of the revolver top latch, and up between the ears of the top strap frame for barrel numbers. Most stocks are marked on the inside of the right one with the serial number also, but not seen on some target stocks.
Let me add a commentary on this S&W that has some additional information.
http://smith-wessonforum.com/blog.php?b=101
I looked at Neal/Jinks book on S&W and got to the list of combination sets for this model. The latest set is serial number 18,873 for the 22 single barrel combination set. That would make the probability that the barrel was added after the revolver left the factory, but never say never. Some exceptions have shown up over the years, so check those numbers.