Shopping cart interaction: how should the user check out?

On our webshop we have a shopping cart icon in the menu bar, that on hover over shows the user what they have in ther cart. Observations in user testing showed that we had a confusing interaction with that hover over. So I'm investigation how to streamline these interactions. So this is the situation:

We have a CTA button at the bottom of the hover over that brings the users to the checkout funnel. And we have the ability to go to checkout by clicking the trolley icon.

We observed that people we confused and start clicking the number to go to check out (that doesn't work) or landed in checkout by accidentally clicking the trolley icon.

Now what would be the best way forward? Make the entire hover over clickable (outlined in green)? Or remove those links and have only the buy button to send people into the checkout funnel?