My perspective is refinishing is a total waste of time and money, very likely costing more than the gun is worth. Run it as is. The sticking of the cylinder has 2 most common causes
Debris ( or even a heavy coat of old sludged up oil ) under the extractor star. Clean this area well and problem may solve itself
Second most common is a loose ejector rod- they were right hand thread up to a point in the 50’s then changed to left hand thread so verify age of gun to be sure ( based on the cylinder possibly being swapped there is also a possibility of a fit issue with the cylinder which would be a bigger headache requiring a gunsmith knowledgeable on S&W revolvers and they are getting hard to find anymore