to the forum from the Wiregrass! You have a S&W .32-20 (Winchester Center Fire) 1905 4th change revolver. The serial number under the barrel should match the number on the face of the cylinder and the butt of the frame. You may have to take the grips off to see the SN on the butt. Be careful, because those grips are fragile. Nice grips by the way. Your gun was shipped in the early thirties..
If you refinish the gun, it will lose any collector value it may have. However, it is not a very valuable gun in the first place. Getting it reblued will cost around $200 from apwcogan.com.