I already answered your question in your support ticket, but I will post my answer also here, so that it will be available for our community.
The header of the RadExpander is placed in a RadToggleButton which means that if you want to expand the content only when the arrow is clicked you will need to modify the ControlTemplate of the RadExpander. In general you can find the LayoutTransformControl with x:Name se to "HeaderContentTransform" and place it inside the toggle button. You can see how to extract a ControlTemplate in the Editing Control Templates help article.
For your convenience I prepared a project with the extracted and modified template.
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