Yeah, I would make it look nice. Make it your own. Don't sand the stock. Use a water soluble stripper. Then see what kind of wood you have. Pick a nice stain or try just True Oil from Birchwood. Bring the metal to the white. Use a solvent to clean the bore, then check the bore if you have a bore sight. run a brass brush only. Oil, assemble, and enjoy.
I bet that stock hasn't had a boiled linseed oil rub for 120 years or more. I'm thinking that giving the stock a little moisture might be a good idea long term with stock being about 150 year old wood. Just an idea...
will be interested in how the adapter works. i have one too also in good shape. seen thie adapter on one of your shorts but they are sold out. on waiting list. btw leave it as is. rare to get a good looking rifle from rti. shame to ruin the history!