Because there are still some challenges getting this done in Photoshop without distorting it in an unwanted way, below is a demo of why you might want to do this in Illustrator instead. If a film frame is set up as a Pattern brush, it distorts to fit the circle, and its overall proportions are maintained as you adjust the thickness using the Stroke value alone. No math required.

I’m not sure if this is exactly how you want it thinner, but my approach shown in the demo below uses these steps:

1. With the Ellipse tool in Path mode, draw an ellipse that tracks the center of the current filmstrip ring. You can also use the Elliptical Marquee tool, but I think paths are easier to adjust precisely. 

2. Duplicate the original layer. 

3. With the layer duplicate selected, convert the path to a vector mask for the duplicate layer. This masks off everything outside the elliptical vector mask.  I used the shortcut of Ctrl-clicking (or on macOS, Command-clicking) the Add Mask icon with a path selected; that’s a shortcut for the command Layer > Vector Mask > Current Path. 

4. Use Edit > Free Transform to proportionally scale the layer duplicate from the center until the overall graphic appears as thin as you want. 

In my example the sprocket holes are not proportional at the bottom, only because I did it too quickly. If you take more time to scale the layer copy more precisely, you can get that part right. 

With this method the frame sizes don’t change so frames appear longer. If you want more control over how it scales, maybe redraw the whole thing in Adobe Illustrator, for example, by creating a custom brush for an ellipse stroke, so that you can easily update it to make adjustments of any kind. You would draw just one frame, and use either of those features to repeat the frame around the circle.

You can make it thinner with Distort > Polar Coordinates, first Polar to Rectangular, scaling the result, and then Rectangular to Polar. Unfortunately, the spacing of the sprocket holes starts looking weird —

How much do you want to reduce its width?  Tell us with reference to the original width i.e by half.

Right now the only way I can think to do it would be to rebuild (illustrate) one frame, and use transform step and repeat to make the circle.  A bit of work, but good practice.  I will be very interested to see someone has a way to do it to the existing graphic.