Open the Cinema 4D menu Window > Customization > Customize Commands.... Use Name filter to find your script. Drag the button to the toolbar and close Customize Commands.... window. If the button contains only one preset, the program will execute it, but if there are more presets, an additional pop-up menu will appear.
When you press a button using the keyboard shortcut Ctrl+Alt+Shift, the presets will be activated cyclically one after another without a pop-up menu.
To get access to the description of the button, you need to click on it with Alt+Shift hotkey pressed.