For light surface rust, I prefer not to use steel wool, which can scratch the bluing. Go down to the super market to the cleaning supplies department and get some brass wool or copper wool that is used for cleaning pots and pans. Use that with oil and I think the rust will come off with minimal damage and no need to cold blue anything.
As to cleaning, what exact model is that gun. There are a few Winchester .22's that can't be cleaned from the breech, but that is the way to clean a rifle if you can. Since they had non-corrosive ammo way back in the old days 30 years ago, I doubt that the barrel has anything in it except dirt and dust. If you do buy a steel brush, use it only if you have to; .22 barrel steel is fairly soft and can be damaged by a steel brush.
Jim
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