"Are cylinders on S&W revolvers interchangeable? "
Absolutely NOT.
Cylinder assemblies, (the cylinder and ejector) are hand fitted at the factory.
This is an extensive process, and the fitter is a true expert that really knows what he's about.
While you'll hear from people who'll tell you that they "dropped-in" a cylinder and it "worked fine", upon examination by an expert, he'll tell you just how and why it really isn't right and does NOT fit properly.
There's a whopping difference between going into the gun, and fitting and working RIGHT.
The difference is in safety, accuracy, and spitting bullet metal.
Once a cylinder assembly is fitted to a frame, it's not likely to properly fit another frame.
Of all the guns I've seen in which a non-EXPERT pistolsmith installed a cylinder, I've NEVER seen one that really fit and worked properly.
Because of the safety aspects of installing a cylinder assembly, most gun companies will not sell a cylinder or ejector to anyone but a factory qualified pro.
Used cylinders and ejectors have already been fitted, and usually can't be re-fitted. Once you remove metal to fit a cylinder assembly, there's no practical way to put metal back.
My advise. Cut to the chase and send it in to S&W and have them install a new assembly the RIGHT way.