It's not possible using existing infrastructure. Windows has built-in support for keyboard shortcuts, but it doesn't work for mouse buttons, so this would need to be done using a system-level hook or some other hack, maybe even depending on mouse manufacturer/model.
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bind your mouse button to a key combination
I do this already. But some combinations are used by other programs, too.
Use a key you can't push directly then. I doubt any program uses F13, for example.