Hi! Can you please help me finding a good low power replacement for a 5V mechanical Relay in the following diagram.

This is a solar powered (with a backup Li-ion battery) project and supply is managed (using MCP73871 chip) and regulated to make it steady.
Timer is generating square pulsers. Every T minutes arduino is switched on for few seconds (~25s) using the Relay. But relay is using quite amount of power. Because this circuit is powered 24x7, relays power consumption (~70mA) really matters.
Therefor is there any substitute that is equal to a mechanical relay that has very low power consumption?
I found that SSR ICs, OptoMOS Relay ICs and Analog Switching ICs can be used but i'm not sure about there power consumption.