First: what are the hypotheses behind the new CTA button? Why do you want to introduce this new component? What is the desired outcome?
Second: it is a quite common, but not so mentioned side effect of CTA buttons, as they purpose is to drive the visitor/user/customer to a specific direction instead of visiting other pages on your site. This is why they are called "Call to Action" buttons.
So, what was the plan with the new button? What are the KPI's behind it, and most importantly, why it "hurts" your business if the CTA performs well?
I think, you should prioritize and determine what is the so called red-route on your website. If the CTA button is not part of the red-route but other section what you mention is part of it, then something went wrong during the design process. "Red routes are the critical tasks that deliver the most value to your users". If introducing a new CTA button impacts badly your business, then you should work on this problem first.