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step-up or joule thief or.. ?

I`m trying to convert the wireless doorbell outside from battery to a renewable source such as solar or wind. My problem lies in that the battery required is a 9v.

My first thought was to produce a high enough voltage to charge the 9v but that might require more solar panels than I have. The 2nd idea was to use a lower voltage battery or super-cap as replacement and stepping up the voltage to 9v. I haven`t taken any measurements of current usage but I don`t imagine it could be more than a couple hundred mA while pushing the button and much lower in idle.