I recently obtained an old Remington Model 4 family heirloom "crack shot" wall hanger.  Years ago I'm told that it blew powder in a shooter's face, so it was disabled with the intent of it being a permanent wall hanger.  The hammer has no spring tension and something was lodged in the barrel so that cartridges cannot be loaded.  I don't think I'm too worried about trying to get it back into shooting condition, but I would like to clean it up and make it a wall hanger.  Here's a few pics:
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So my general plan is to take it apart and clean all the surface rust off as best I can without damaging any bluing that is still remaining.  In the past I think that I have seen recommendations (and used) 0000 steel wool to just rub oil on the steel.  Unless I'm told otherwise, I planned to go this route, along with hitting the nooks and crannies with a toothbrush and some very light work with a dental pick in areas that are really hard to get to.  Any other advise or reasons to do it differently?

Also, any suggestions for cleaning the wood up?  

Really, it could go on the wall right the way it is, but I figured cleaning it up some would be a good excuse to play around with it a bit.

Bronze wool rather than steel wool.

A copper penny and oil for tough spots.

A plastic pick rather than a steel pick.

Thank you for the quick reply, I will pick up some bronze wool and some plastic pics.

One more before pic from when I tore it apart:
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I ended up soaking the steel parts in PB Blaster and oil, bronze wooling and working over with picks and Q Tips until I had the all of the heaviest easiest to remove rust.  I rubbed the stock down with denatured alcohol several times and steamed, which brought quite a bit of "gunk" out of it.  Then I lightly sanded and rubbed on 3 coats of tung oil with some light 0000 steel wooling between each coat.

It's still got plenty of "flaws", but I got the heavy knocked off:
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ETA: dang that's a horrible potatoe pic...