I think that could work. Depending on the size, you could get a large amount of power from a steam engine, which means you may only have to run it for a short time each day to fill the batteries.
An alternative is a very small steam engine, with a fire you keep going constantly. But that is a lot of work - it might cut into your sleeping time!
We have got so used to power at the flick of a switch, that I think one needs to plan something that is relatively automated, otherwise you will just stop using it once the novelty wears off.