Dear OP,
Hope my experience helps you if you decide to cold blue your revolver.

A while ago I bought a beat up Maverick 88 shotgun, and I reblued the barrel and mag tube using Birchwood Casey Gun Blue Kit. It's a 3-piece kit that comes with everything you need.

You strip the old finish, thoroughly sand and polish, degrease and then cold blue.

It sounds easy. Well, it's not.
It took me one barrel to realise I didn't want to do it again. You apply coat after coat after coat and it looks like it's never getting darker. Really frustrating.

And the results are mediocre. It's a thin, blotchy looking finish.
Doing a revolver will probably be 20 times harder than a shotgun barrel.

That product is for touch-ups, not entire firearms.

This was what I accomplished, it was almost 8 hours of work.




For a cheap shotgun, it looked OK.
For a S&W Model 13, I'd probably leave it as is. But it's your choice and these were only my 2 cents.

Enjoy your new revolver!