I want my Mac Mini power button to shut down the computer
I'm not aware of a way to make the power button tell your Mac mini to perform a normal shutdown, however one solution that comes to mind (assuming you have an iOS device) is to shut your Mac mini down from your iPhone or iPad using an app like iShutdown.

There is a small application that you install on your Mac.

And then you have the app on your phone that has a list of computers you can shutdown and a big virtual power button for each.