Not knowing anything about wood stoves, I can see where your reasoning makes sense.
As long as the mechanical pieces of the fan are heat resistant, and as long as you have a way to clean and grease/oil the fan on a periodic basis, I see no reason why putting one in the chimney wouldn't work. As long as the wires to the solar panel are properly insulated, and the panel itself is out of the heat zone, I can't see anything wrong with your theory.
If you do it, please take lots of pictures and keep us updated!