If you have basic metal working facilities you aren't far from being able draw wire and then you can make relays. It might take a while to replicate Konrad Zuse's machines but I think that it might be simpler to do that than go for purely mechanical computers, see https://en.wikipedia.org/wiki/Z3_(computer)
And of course the serious calculator enthusiast would have a Curta. Needs a bit more than basic metal working I suspect: https://en.wikipedia.org/wiki/Curta