Would the FE1, FE2 or FE3 struts fit on the CTS-v?

Obviously I'm not looking to get rid of my magnetic shocks. I have a VERY small driver side front suspension noise that is driving me nuts. I been at it for over a month and cannot figure out what it can be. I'm left thinking it can be inside of the shock. I don't want to pay well over $300 for a CTS-V strut to only find out the noise is coming from somewhere else. I can probably pick up a used CTS strut of under $100 and see what happens.

So, would it fit?