There is one way you can do this. For the server version, create a constant in the workflow settings:
You can then wrap the email output into a macro and feed this constant value in as a batch parameter. Connect the batch parameter to the container in which your email tool sits. Use the action tool to switch the button off if the constant does not equal "Server".
You can then lock the macro so the designer users don't have access to see the logic that is disabling the email.
You shouldn't need to create your own constant and have two versions of the workflow. You can use the Engine GuiInteraction constant:
GuiInteraction: A Boolean value indicating whether or not a workflow is being run from the GUI. When a workflow is run from the Alteryx Designer or Analytic App interface, the returned value will be True or 1. When a workflow is run from command line, the returned value is false, or 0.
So if running from the Gallery, the value will be False / 0.