The minimize button is part of the stack presentation and cannot be removed easily. You would have to write your own presentation.
The above said applies to the 3.x workbench. If you are using or can upgrade to RAP on e4, it should be easier to style certain aspects of the workbench without re-implementing large part of the presentaion.
Or - my recommendation - reconsider if using the workbench in a web application is the right choice. You can also use RAP's SWT port RWT and JFace alone to build web applications that more closely match the expectations of web UI users.