Not an external hardware solution but what you can do:
Create a barely visible, overlayed software button that can be freely placed around the edges and can be tapped to mute/unmute sound.
- A mute/unmute workflow (with restoring the previous volume) can be created with Shortcuts and even triggered by a Siri command (it can also be displayed as a widget or Home Screen icon).
- Activate and place the 'AssistiveTouch' button on an edge. A simple tap on it can mute/unmute the sound by assigning said workflow.
- Configure 'Triple-Tap-the-Power-Button' to hide/show the 'AssistiveTouch' button if its presence is not desired.
1) Activate, then assign 'AssistiveTouch' button to workflow:
Settings > Accessibility > Tap > AssistiveTouch > Single Tap > 'your workflow'
and
Opacity > 15 %
2) Assign 'Triple-Tap' to show/hide the 'AssistiveTouch' button:
Settings > Accessibility > Shortcut > AssistiveTouch
I can create the workflow if you’re interested.
EDIT: One if the bazillion bugs of iOS/iPadOS 16 prevents the 'AssistiveTouch' button from showing reliably in landscape mode (at least on my iPad 6th gen). Turning the iPad to portrait mode and back makes the button appear… 🙃