In your DishonoredInput.ini file, add this keybinding: m_PCBindings=(Name="F1",Command="set Console ConsoleKey F1")

If you then launch dishonored and press F1 you will have the console set to F1 (confusing, I know, but it works). You can change either of the "F1" values if you want these on other keys, check the D1 setup guide for more info.