Schottky diodes in series to reduce maximum voltage at supercapacitor solar charging circuit
Voltage rating of the super capacitor is as important as the operating temperature specification. The higher voltage leads to significantly higher self discharge.  

Adding a second diode will definitely help to keep the voltage applied to the super capacitor within its operating condition. I don't see any disadvantage because of the secondary diode addition for the presenter circuit.  

One suggestion is to employ a low leakage diode instead of two Schottky if feasible. It will less discharge the capacitor when the solar voltage is not present.