Either blue, white or brown.
Most of the half stocks look very nice with a browned finish. Yes, that is putting rust back on the outside of your barrel but there is a difference.
Browning is a controlled rusting process that produces a very hard rust. One that looks uniform, holds oil to prevent further rusting and prevents glare that often is noted with blued barrels.
Bluing unfortunately is not an easy option.
Yes, there are cold blues that you can use but these are very thin and usually will wear off in a short amount of time.
There is a hard rust bluing where the barrel is first browned and then boiled in purified water (before oiling).
That changes the brown rust to a black rust that is often called "bluing".
You could leave the barrel "in the white" and just lightly sand it with some black silicone carbide wet/dry sandpaper (320 grit) and then let it "age" to a somewhat used look.
Some folks who want a worn look will use weak acids to produce a gray look but in my opinion that makes it look like it is a poorly cared for gun. Different strokes as they say. :grin:
If I were you I would give strong consideration to browning your barrel.
I would also NOT recommend using Birchwood Casey Plum Brown to do this.
The slower products like Laurel Mountain "Barrel Brown & Degreaser" is non toxic and easy to use if you have access to a steamy bathroom or any other place with high humidity.
It can be bought at Track of the Wolf for very little money.