Ok, I have some fan specs for you-
AcuRite 5n1 Aspirating fan
Rated voltage : 1.5V
No load current : <20mA
A 3.0V power supply would be fine to replace the solar panel and power the fan directly, although the fan was not designed to run constantly, so I am not sure how it would affect it's service life.
DISCLAIMER: Please note that modification of the 5n1 assembly will void the warranty, as is customary with electronic devices. Chaney recommends that you DO NOT modify the weather equipment in any way- and Chaney cannot be held liable or responsible for any modifications, or injuries or negative effects that may result from any modifications performed by a customer or user in the field.