Smith & Wesson snubbies are not inaccurate, most users just can not make good use of the fixed sights
I started carrying a 2" Chiefs Special Target when they became available in stainless back in 1985. I have no problem making head shots on a B27 target at 25 yards with the little J-frames.
The red ramp insert was added to the Model 60 CST that used to live in my ankle holster. It brought the sight picture into my line of vision faster than the all stainless front sight
The only thing that has made me move away from carrying the Model 60 CSTs is the J-Magnum revolvers introduction in the late 1990s. So far Smith and Wesson has not released a 357 Magnum version of the Model 60 Chiefs Special Target or I would be carrying it
I have never owned a Model 12 but I do have it's predecessor, a 1953 manufactured Airweight 38 M&P with the aluminium cylinder
If you can not shoot a 2" Model 10 well, then you will have the same problem with the 2" Model 12. As Model520Fan mentions, the Model 15s will shoot very well. Again this is due to the better sight picture and not some difference in the revolvers design.
Most all 2" Smith & Wesson revolvers will shoot superb groups from a ransom rest. The issue is not the revolver it is the sights that we as humans just can not get a good enough picture from.
The Model 27/327/627 family of revolvers are all very fine choices. I am guessing that you are referring to the 2 5/8" Model 627 Ultimate Defense Revolver hat was introduced in 1999
I changed the factory supplied grips to a nice set of Factory round butt combats.
If you still want a lightweight solution, there is the 2 1/2" 327 Nightguard. While the Cylinder and slide supplied Extreme Duty sights provide a better picture than a groove milled down the top of a frame, they are not as precise as factory adjustable sights.
The good news is that a Factory adjustable sight can easily be swapped in on a Nightguard