Here's an alternative:
If you have a Ring alarm system, you could use a door/window sensor to trigger a routine. So you could place one of those small magnetic sensors next to the phone. If it's a confidential call, move the magnet away from the sensor and your "do not enter" signs will turn on. Move the magnet back and the signs turn off.
I imagine other sensors can do the same. But keep in mind that not every sensor or manufacturer are supported and only certain ones can be used as a trigger in Alexa routines. I only mention the Ring alarm window/door sensor because I use it myself and it can be used as a trigger in routines. For example, I have a routine that is triggered by a Ring door sensor at my front door that announces "front door open" whenever someone opens that door.