If this is really a concern,
you should look into rocket stove “technology”.
Minimal wood, minimal smoke, maximum efficiency (due to very high draft).
As for the generator fuel question, you’d best be experimenting with wood gasifiers if you plan on using a generator after fuel supplies are kaput.
Best be careful while doing that. I have burn scars down my neck and back after one barfed its charcoal out the top like a volcano.
Fastest I EVER shed a shirt and jacket and rolled in the snow.
/johnny