<control>:SetHidden(true)
<control>:SetMouseEnabled(false)
Move your mouse above the button, use merTorchbug or Zgoo and type /tbm or /zgoo mouse to inspect the control and you got the name.
To do that as the armory opens check what scene it uses, e.g. by using /tbsc with mertorchbug to see the SCENE_MANAGER and check currentScene entry.
Use the scene state change callback, or a fragment if the scene is the armory scene but the button only shows at 1 fragment of that scene, to hide and/or show it according to your needs.
https://wiki.esoui.com/Scene_Manager:_On_scene_change
https://wiki.esoui.com/Fragments_in_...t_state_change