Ken is correct on the "Brown" of the barrels. This turning to brown over time is one reason so many do not realize that most US doubles were finished in black & White.
Personally with that much original finish remaining I would preserve it rather than refinish just to get the "Correct" black finish. It is of course your gun & you can do as you please with it. What you have now though certainly appears to be original finish, a refinish would not be.

Miller/TN
I Didn't Say Everything I Said, Yogi Berra