Suggest that you do nothing to the gun in the way of restoration. It is a good historical relic as it is and to change it wipes out that record of use. The 1842 is not a high value gun and you will not gain from an expensive restoration, in my opinion. Rather, see what you find out about its history as to who used it, and how it got to where it was found. You may have a jewel in it.
As an example similar to your situation, I knew a fellow who found a Gumph Lancaster rifle out west.
It was covered with leather and brass tacks which he did not like. He told me that he stripped all of that off and refinished the stock. When I told him what he had done he was pretty crest fallen. He had taken a genuine Indian gun and undid its history; he reduced its value by about 75%. Just my thoughts on the matter.
Dick