Christoph The point for me with the left or right border is, that the navigation arrows keep being visible. Maybe it's generally possible to hide everything, if the mouse is not being moved.
I understand your issue. The problem is that all these interface elements will remain visible on mouse hover for good reason ... If the visitor mouses over the area that defines click "next", it's normally useful that the "next" icon remains visible, to emphasize the action that occurs on click. It's a bit unusual to require a "no-cursor" state, but almost anything is possible with some custom CSS, although it would involve some compromise to the interface ...
For example, we could add some CSS that prevents the caption from remaining visible on mouse hover. And in the same action, we could also hide the cursor. This would mean that you could move mouse over caption, and within a few seconds of inactivity, the caption and cursor would disappear. Of course, this would mean that user can't keep the caption persistently visible, unless the lock it.