Not a S&W product. The Baby Hammerless revolvers you describe were made by Kolb. Value under $300, much less if it doesnt work.
You can start by checking firearm databases like GunBroker or Armslist to see if any similar models are listed. You could also consult with firearms experts or visit gun forums to gather more insights. Additionally, you may find relevant information in vintage gun catalogs or through historical firearm research.
There have been a number of "hammerless" revolvers made, ranging from the tiny Baby Hammerless .22, thru the Iver Johnson and US Revolver Hammerless topbreaks, and includinurrent day Smoth & Wesson revolvers. All DO have hammers that are internal to the handgun frame.
The Kolb Baby Hammerless revolver was made in several different variations. Value will depend on exact model, and condition. IF yours is in firing condition, it may be worth $200-$400. These did not have very durable springs- they break easily. They were the smallest double action revolver made.
There is no real limit (other than practicality) of the smallest gun you can own. The smallest caliber firearm I now own is a .17 HMR. The smallest physical size is a Baby Hammerless revolver from 1920. It is a .22 Short revolver that is about 4.5 inches long, and was made to fit in a vest pocket. There ARE smaller guns.
No way to answer without a DETAILED description of ALL markings.
100-300 usd
One
100-1000 usd
I recommend to look on gunbroker.com, as these parts come up regularly. Also numrich sells parts, but many may be "out of stock".
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No such model listed in the Standard Catalog of Smith and Wesson. You need to call the factory
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The value of ANY gun is based on the exact make, model, and condition. The Baby Hammerless was not a derringer, but a very tiny revolver with a folding trigger. The value of those revolvers runs about $200 for a working specimen in fair condition. Do NOT attempt to fire this with modern high speed 22 Shorts- it was made for black powder cartridges. Better condition can equal higher prices.