You can use a mouse button as the hotkey for a mapped key within IS Boxer just fine.
For some reason, outputting the mouse button as part of a mapped key doesn't work consistently.
But if you have IS Boxer send a key combination to warcraft, that always works.

I've got one mouse button which is tied to FTL Follow Me.
And another which sends Shift F7 to warcraft, with a variety of things there, such as a Druid macro to Cat Form if not in Kitty and then Stealth if in Kitty.