Can one build a "mechanical" universal Turing machine?
Sure. Electricity is unrelated to the model of computation.
The only thing you can't actually build is the infinite tape, for obvious reasons. In this sense, anything that can be built is essentially equivalent to a deterministic finite automaton.
Here's a Turing Machine made of wood:
https://www.youtube.com/watch?v=vo8izCKHiF0&amp;ab_channel=RichardRidel