Category dropdown list (no submit button)

I’d like to make a dropdown list that displays every category (hopefully every non-empty, but that’s not as important). Furthermore, I would like for the user to immediately be directed to the category page upon clicking it in the dropdown – no submit button.

I’ve looked at the dropdown_cats() function, but apparently there is no way to do it without a submit button unless you edit the core of WordPress. Does anyone know of any plugins or workarounds to get this working?