[Arran]

They did use stains, or dyes, back then, but I think they used some sort of paint or sealer on the insides of cabinets. It may have been a mix of hide glue and a dye in some cases. Flat dark brown paint would be fine, like dark brown Bakelite colour, you don't have to be 100% accurate, I doubt if every cabinet of a given type was exactly the same, it probably varied from day to day, week to week, depending on who was doing the mixing, or what lot they used.
Regards
Arran