I am going to presume from the total lack of responses that no one else has actually found any documents supporting the use of acids, shellac, or varnishes in the colonial gunsmithing shops. I have seen some reference to varnish in the cabinet maker's inventory. Cabinet making is arguably not a frontier activity.
So it would seem the traditional finishes of linseed oil, beeswax, soot, stale cow urine and iron filings may well be the historically correct candidates. I would note that all of these components are byproducts of common frontier farming activity and ready at hand.
I am no expert but here goes anyway.
Oil or paint pots may be for "boiling" (actually just heating) Linseed oil to add drier metals and resin, usually Rosin or Gum Arabic to make drying oil and varnishes. Some limestone, crushed, helps kill organic acids in the oil and helps drying. They may gave used lead oxides as well back in the day it reddens the oil and helps drying in high humidity or so I have been told. But its not a good idea today.
Drying oils and varnishes were made in small batches. to prevent loss to setting up in partly filled container.
I am sure they had Nitric Acid which was common and other such things. Some sort of flux for soldering, an acid might work for lead based solder. A flux for brazing brazing and something for forge welding but would have to dig into some old blacksmithing book to find what they may have used. Don't know how common borax was at the time.
Beeswax is not a finish for wood, not a good one anyway.
Cabinet makers and instrument makers may not have used varnishes that would work well for a firearm that was routinely subjected to the weather.
The next thing is that some of the chemicals may have archaic names that would need research to find what it actually was.
Dan