Advice needed: Creating an empty point in the centre of an object

Hi, I wonder if anyone can help. I have a document with a series of (many) circles —kind of like a halftone pattern. I'm planning to pen plot this image but I don't want the pen to draw the circles, but to simply place a single dot in the centre of each circle. In order to do this I think I'll need to put an empty point in the centre of each circle. Is there a way to do this? Maybe using a script? I've attached images here

This is a crop of the artwork

This is what I want to do. Place a point in the centre of each circle and then delete all the circles.