Can I change monitor volume with mouse buttons or wheel shortcuts?

Yes. Use a mouse utility that can invoke a macOS Shortcut or shell command, and have it call BetterDisplay’s volume adjustment for the intended display. BetterDisplay supplies the display-control action. The mouse utility recognizes your button or wheel gesture.

In Shortcuts, add BetterDisplay’s Image Adjustment Offset action. Despite its name, its Feature list includes Volume. Select the display and use an Offset Value such as 5 for volume up or -5 for volume down. These are percentage points of the control’s range. Create separate shortcuts for each direction and test them manually before assigning mouse gestures.

If the mouse utility sends keyboard combinations, assign each shortcut a keyboard combination and map the gestures to those combinations. If it can launch shortcuts directly, select the corresponding shortcut there. See display-specific shortcuts for keyboard assignment.

For a utility that runs shell commands, the equivalent CLI adjustments are:

betterdisplaycli set -name="Desk Display" -volume=0.05 -offset
betterdisplaycli set -name="Desk Display" -volume=-0.05 -offset

Replace Desk Display with the intended display’s distinct name. Install the CLI and keep BetterDisplay running as described in CLI setup and examples. A mouse utility may need the CLI’s full executable path if its command environment cannot find it.

The display needs a working volume-level controller. Confirm that its BetterDisplay volume slider works first. Percentage offsets are not the same as a remote that only supports volume-up and volume-down buttons. You do not need a second display-control app solely to translate mouse gestures into these actions. The exact gesture assignment depends on your mouse utility.