Hello again,
Thanks for the pictures. That gun you got at a pawn shop is the iconic Model 36 all right, and I would venture that the Smith & Wesson Model 36 along with the snub nose Colt Detective Special, were probably carried by literally thousands of LEO's either as primary duty weapon, or BUG in maybe an ankle holster.
Your gun looks very lightly used. The finish is fine..I for one would not recommend any sort of refinish by anyone. Your stocks are known as PC, meaning Plain Clothes from the rounded shape at the bottom so as not to snag on coats (from the days Detectives, Chiefs, LEO's working undercover, etc. all USED to wear coats and ties!).
If you obtained that gun for around $400 or less...you did great in my opinion.
One more "tip". If you are a shooter and will be shooting that Model 36 be aware that it is not rated for the Plus P ammo. That doesn't mean it will blow up on you first time out, just that it was intended and designed for 38 Special ammo (I use Magtech 158 grain, FMC-Flat nose for practice and carry).
I started concealed carry in the late 1960's and my first carry gun was a Model 36. When the Model 60 (same gun-stainless steel) came out I carried that until about 2002 when I got a Model 637-2 which was the first Plus P rated gun and that became my EDC right up to yesterday (only cause I haven't been outside yet today

).
Enjoy that one of yours....get ready for the big circle of fire out of that snubby barrel, especially if you shoot indoor range where it is darker!