Ok, so $10 per battery at 50 unit quantities.
It's hard to tell how well the battery will stand up to its capacity rating or age over time but we can say it would last 2 years as a worst-case scenario.
Over a 10 year period that's $50 in batteries plus needing to arrange for a worker to go out and replace them 5 times over the course of 10 years which they can pay a worker to do for free but it will eat up about 10 -15 mins of their time to actually get out and do the swap.
You have to dispose of a toxic battery 5 times over a 10-year time frame also.
I bet a solar panel and battery combo could be added for $15, in higher quantities. The solar panel does not need to be large for this application so it could be a very small custom panel. Something like the Voltaic Systems 1w Panel.
With the low discharge rates, the battery can be small and would last a very long time if a quality cell is chosen.