I have found some regular timers with electronic clocks that say they can hold the clock for up to 96 hours in a power failure. That might the trick.
The thing with battery back up devices is they are not typically design for multiple and or long power outages. For example a resi smoke alarm. The battery carries the device but can do it for about a total time of 8 hours and it does not recharge the battery like a fire alarm panel battery. It's is important to to see how the battery is used for the device. If the switch recharges the battery then that would be a great and economical option. A battery operated timer would require a regular battery replacement and it wouldnt be well liked by the customer
Also using any device in a way not intended may void the listing and warranty
