I'd leave the finish as is rather than trying a cold blue product. If you keep it oiled or waxed you'll be fine. Worst case scenario is that it develops a patina. If you are planning on carrying the gun regularly i'd do something and i'd choose something better than cold blue for an entire gun.

I view cold blue like I view touch up paint for a car. To cover up a small nick is fine but there's no way I'd try and paint an entire car door using touch up paint.

With a gun like that the only thing that matters is how it shoots. If you want a better looking gun sell that and put the money into something nicer.