Alexa routines cannot be triggered by any button excpet the Amazon button at this time. You can trigger based on virtual motion sensors running on the SmartThings cloud for now. I do this for TTS announcements from Alexa. This requires you somehow trigger the virtual motion sensor.
I do this by having Google Assistant trigger a virtual motion sensor that is exposed to the SmartThings cloud as a switch. Hubitat turns on a DTH that is a vitual motion sensor, but operates like a switch. I do this with Google Assistant Relay, which is an awsome tool to have at your disposal for many more reasons than just this one. The setup is very reliable (and the irony that part of it is on a Samsung Cloud server isn't lost on me), and works within a few seconds.
So, I don't know if you're up for it. It's not a one day project for a beginner, but if you had Google Assistant Relay running, what you would do is make a RM rule that, when you press a button on your switch, Google Assistant Relay would (silently) tell SmartThings to turn on the "virtual motion sensor as switch" device. Then Alexa would detect that that virtual motion sensor had triggered, and execute the routine.
