Show my mouse cursor while a presenter sharing screens

Hi. I teach programming on 1on1 zoom call. I'm a licensed zoom user. A student shares their screen to show their text book and source code. Is it possible to show my mouse cursor on a student's shared screen? I often want to point what to correct in their source code, where to read in their text book. I always use annotation tools, but if I can simply share my mouse cursor, it would be nice.

The reason I don't share my screen is that my students don't have a screen big enough, and I need see what they are writing.

Thanks!