Some googling and I found a related paper: "Accuracy of Smartphone-Based Pulse Oximetry Compared with Hospital-Grade Pulse Oximetry in Healthy Children"
DISCUSSION AND CONCLUSIONS: Smartphone-based pulse oximetry is not inferior to standard pulse oximetry in pediatric patients without hypoxia. [1]
However in this case you _are_ trying to test for hypoxia...
Another link answering the question "Should smartphone apps be used as oximeters":
CONCLUSIONS
It is not physically possible to measure SpO2 using current smartphone technology. The two published studies which assessed smartphone oximeter apps (Digidoc and Samsung) raise serious questions about the diagnostic accuracy. The Samsung app has been withdrawn, and the claim that oxygen saturation can be measured indirectly through “stress assessment” is false. [2]
[1] https://www.ncbi.nlm.nih.gov/pubmed/29215972
[2] https://www.cebm.net/covid-19/question-should-smartphone-app...
If you've got $300 to spare, this one is allegedly FDA approved: https://www.masimopersonalhealth.com/products/mightysat-fing...
Also, this article mentions that people are subconsciously altering their breathing/heart rate when affected. If you already have a smart watch that is tracking your heart rate, you may be able to infer this condition by monitoring heart rate deviations from normal.
In addition to having the alarm that you need for sports, it can also track heart rate and log your data. Later, you can then connect it via USB (or Bluetooth if you buy the upgrade) to do interesting analysis such as correlating your pulse and oxygen saturation with the route that you drove (mountain bicycling).
It's super nerdy, but a great toy for making your exercise feel like science.
Model 500E which was recently released then. It is rated at 2% +/- but their documentation says that their lab testing gives 1% +/-
Does not have memory as I did not need that so you will be able to spot check and not have, for example, overnight readings.