Poor question. Hard to understand.
After sticking with it for longer than I think most people would (screenshots would help immensely), I think I have some idea of what you're asking, and I don't see why anyone would want it. Another reason for people to answer something else and not this one.
Why do you want a black screen with only a mouse pointer on it? What use is that?
I suppose you could use a presentation program of some kind to create an all-black slide and show that full-screen, then have OBS capture that plus the mouse pointer. At that point, a window capture might work better than a screen capture, because it allows other windows to be on top of the captured window and still capture the correct one.
