Effect on battery characteristics of a zinc-air button cell from oxygen starvation?
So as it turns out zinc-air button cell batteries can be utilized as oxygen sensors by monitoring the current and voltage characteristics when driving a load as indicated in the two related patents below - there has also been an academic study done on effects of low oxygen environment to zinc-air batteries but I do not have access IEEE paywalled paper: Oxygen consumption of zinc-air batteries and their performance at low oxygen concentration levels (if someone with access is able to summarize the finding in the comments I would be most grateful) :

Patent US6758962B1: Oxygen sensing  


  Oxygen concentration measurement is carried out over a broad range by an instrument utilizing a zinc-air cell having a lower-than-nominal potential difference imposed across its electrodes by a shunt branch incorporating the source-drain circuit of a field effect transistor (FET). A feedback circuit is used to improve linearity of the output and cell life without sacrificing the broad dynamic range achieved by the use of the FET shunt branch.


Patent US6099707A: Apparatus for sensing oxygen concentration


  An apparatus and method for sensing a concentration of oxygen in a flow of gas in a breathing circuit for a patient. A biasing voltage is provided across a zinc-air cell so that the zinc-air cell produces a current having a magnitude, wherein the magnitude of the current corresponds to the concentration of oxygen in the gas.