I am looking for a way to change the bouncing cursor that appears when an application is launched into a loading cursor. I know that the bouncing cursor can be disabled, but I could not find an option to replace it with the loading cursor. Is there any way this can be done?

I can't find that option either (maybe it's because the loading cursor is supposed to show the state of the current application or something like that). Have you tried the "Passive Busy Cursor" option? It shows the application icon next to the cursor.

I would suggest trying the "Passive Busy Cursor" or "Blinking Cursor" options, although the Blinking Cursor option will still use the application icon (but it will blink instead).