If you think you draw a lot of power now, wait until you add a relay! If you were to go down that path, use FETs as switches, not relays as relays are serious power hogs.

But there is a simpler way. Pin 5 (GP2/INT) can be configured to be an external interrupt. So rearrange your hardware to connect the switch there, then in your software, simply put the device to sleep, drawing nano-amps, until a switch transition generates an interrupt and wakes it up. Then run your routine and go back to sleep, waiting for the next interrupt.

Details are in the datasheet.