Unless there is a state or local law it can be sent from an individual to another individual, with no FFL or C&R required. This is wny many prople collect antique (pre-1898) guns rather then later ones. USPS, will accept antiques for shipment between unlicenced individuals, but not post-1898 firearms.
So as an example, I live in Arizona, where there are no legal restrictions on antique firearms. If I wanted your gun I could send you a certified check, and then you could send me the gun. It would be shipped as an Antique, not a Firearm.
However once it is entered into a FFL or C&R licence holders "bound book" the BATF&E will expect it to stay "on paper" and it would no longer be attractive to many collectors (read that as well funded buyers) because of this.
If your potential buyers lives in a gun-restrictive state or city, such as NYC or Chicago, or a state like N.J. there could be a problem. If however he lives in most of the United States, and some foreign countries there wouldn't be.
If Gunbroker.com had listed the revolver in the Antique Section this matter shouldn't have even come up.
It is possible that the New Model No. 3 is listed as a C&R, but I doubt it, and if it is it shouldn't be.
Incidentally, post the serial number of your revolver, using xx for the last two numbers. You need to know when it was made, not when it was originally sold.
A call to Roy Jinks at S&W will confirm that all of the New Model No. 3 frames were made prior to 1898.