I might try desoldering as I don't have problems with understanding it and there are no SMD elements. I just wonder how will sensor act without the temperature. 
How much data do you guess you need of the humidity only?
I might also look for some old AA batteries to test the indicator. I don't have laboratory PSU, only one running 3.3V but might to try get voltage down with resistor or sth.
Weather station only shows 'low' battery (if its good, nothing shows up).
Regards