Whenever you run a workflow, Nintex displays a diagram of the workflow on the right side as part of the initiation form - in most cases, this is great as it serves as a quick visual reminder of what workflow you're about to kick off. However, if you really want to hide everything on here, the only way to do this is to customize the InitiationForm.
If you take a look at the url of the browser, you'll notice that the Nintex Workflow loads at http://[my site]/_layouts/NINTEXWORKFLOW/StartWorkflow.aspx - so all we need to do is make a copy of this form that doesn't include the diagram, tell the workflow to use our custom version, and we're done!
I would recommend copying the form and including it in a mapped Sharepoint Folder in a VS2010 project as the easiest way to provision the form to a Sharepoint installation - below I've made a copy and renamed it StartWorkflowNoDiagram.aspx
After renaming all the content from StartWorkflow to StartWorkflowNoDiagram, all we need to do is hide the WorkflowVisualizer control.
I'm not sure if there's a cleaner way to hide it than putting it in a hidden div, but stripping the control out altogether causes null reference exceptions, so I figured I'd rather have the form working than not!
The last thing to do is to point the workflow to use a custom form - this setting can be found in Workflow Settings, right at the very bottom:
In my case, because my version of the StartWorkflowNoDiagram page was in a mapped folder, I put the following url in the field: