For the one-button touch to fake a phone call, add a 60-second delay before call happens and don’t touch your watch during that time, for maximum deniability.
There should be delay that is long enough that anyone would forget the rich, but it should also be "random". You'd want to avoid using it too often around observant people (one every two months, maybe). The watch touch and ringing won't give someone away but thier bad acting will.
Surely the real trick is to activate it blindly with your hands under a table or whatever? (Yes, also with a delay so you can have your hands visible when you get the call)
How often are you little in this situation that you need a fake phone call...?
Even if it never happens, it is still fun to think about.
Possibly a lot more if I could make it convincing...