As I understand it, all these Oldham types are lead acid batteries.
Their working electrolyte was dilute sulphuric acid, and as their efficiency diminishes the plates become more covered with unreactive lead sulphate, hence reducing their capacity.
However it is still an acidic environment and I would recommend dropping the inners into either baking or washing soda, solution, before disposing of them.
Naturally wear eye protection, just in case!