Hyperventilation removes CO2 from the blood

...which causes hypocapnia, which can be dangerous if prolonged.

Are you sure? I would expect it to be the response to high co2 levels, since it removes co2.

It's why breathing into a bag works. You need to slow your breathing during hyperventilation to increase your CO2 back to baseline. Not speed it up.

Can CO2 be measured in a simple way? (Like an oximeter in a smartwatch measures oxygen)?

Yes there is some equipment to do transcutaneous pCO2 but that's mostly used in sleep studies AFAIK. Most of the time you use a blood test. I heard in some research they use IR on expired air not sure how common that is. If you find a "home made" way to get a (even just relative) pCO2 reading I would be highly interested.

The desire to breathe in a healthy individual is a really good proxy for CO2 levels based on a wonderful design with distributed sensors throughout the body.

It is not a good proxy for O2 levels in healthy individuals, but may be in people with COPD or other chronic breathing problems.