I used the Rotate tool to distribute copies of the small circle around a large circle. This article will get you going. Basically you alt-click the Rotate tool on the center of the guide circle, hit Copy, and then hit ctrl-D to repeat.
To determine the rotation angle value, I first decided on the physical spacing that looked right to me, say 4mm. Then I figured out the circumference of the guide circle and how many copies of the little circle would fit around it. The value in the Degrees/Rep column are what I entered into the Rotate tool.
The spacing of the small circles isn’t perfect but it’s good 'nuff for me.
Somewhere there is probably a much smarter, faster way to get Illustrator to fill a circle with an even radial array of other circles, but I haven’t found it yet. (I know how to do a grid of circles, but a grid isn’t right for this, it’s just not.)
Here’s the SVG. The disc is 2.653" diameter and the holes are 2.5 mm diameter with 4mm spacing.
shaker print temp.zip (2.6 KB)