Hello,
One option would be to copy our {x:Static dockingThemes:DockingCommonDictionary.StandardMdiDocumentStyleKey} Style and give it a new key, like "CustomStandardMdiDocumentStyleKey". Then you'd alter the control template by changing the setting of StandardMdiWindowControl.CanClose to be StandardMdiWindowControl.HasCloseButton. So something like this:
<dockingPrimitives:StandardMdiWindowControl x:Name="PART_MagneticWindow"
...
HasCloseButton="{TemplateBinding CanCloseResolved}"
... />
Then you'd apply that the "CustomStandardMdiDocumentStyleKey" to the Style property of document windows that you want to hide the close button.
Alternatively, you could create an implicit Style for StandardMdiWindowControl that binds HasCloseButton to a custom attached property on the templated parent (i.e. the DocumentWindow).