Powering a wireless camera
Long story short: There's no free lunch. For every bit you transmit wirelessly, you have to spend energy. The amount of power spent in the CPU is probably lower than what you have to spend to transfer the data.

Not to mention that the camera uses power too.

So: Use the camera and the wifi as little as possible. You probably have enough nice photographs of your bike shed. You don't need to know what it looks like when there's nothing moving in there.

Have a cheap PIR movement sensor, maybe attached to an actual low-power device (not an arduino board, typically these come with a lot of static power consumption, and also, Arduino is terrible at allowing you to actually put the MCU to sleep while you don't need it). With that, power up the camera and the pi only when needed. Suspend the Pi (or completely shut it down) when not in use.


  I considered using an arduino to "wake" the raspberry pi. But with a boot time of around 20 seconds, it could miss crucial footage.


Get a different OS for your Pi. Boot time should not take more than 5 seconds. Also, have you ever heard of someone entering a bike shed and leaving with a bike within 20s? You could easily solve that issue with a low-tech solution like a 3-digit lock attached to a pole or something.