I haven’t found one but I did a fairly exhaustive search a few months ago. The most promising option was this (but it didn’t pan out):
Prices range form $10 to $6.50 depending on quantity.
I ordered a sample button but I could never get it to be recognized on my network and the company’s customer support was very poor. Also, it required me to use the company’s server to route the information through, which I didn’t like.
In the end, I chose to build a software solution that runs on old, cheap screens, like an old iphone5. I wrote a bit about it here:
https://eventloggers.com/blog/turn-your-old-screens-event-panels - there are a few photos.
In addition to the “virtual button” solution, I’m using Google Home/Google Assistant to record personal events. More on that here: https://eventloggers.com/blog/voice-logging-just-got-easier-eventloggerscom
I also teamed up with a friend and build some prototypes but we didn’t have the skillsets or time to scale the project (it was back in 22012) - I honestly thought someone would come up with a solution that I could leverage but so far, I haven’t found one.
I’m still very interested in a physical dedicated, cheap button, so if you find a candidate, please let me know.