My first thought from the title was that there's an option to show the cursor or not. But I see that that's not your issue.
This might be one of a very few cases where a physical capture card does differ from the Display Capture source. So you'd run your physical video signal out of your GPU, into the capture card, and then the passthrough of the capture card goes to your screen. (make sure you get a capture card that does have a passthrough; not all of them do)