Is this not the same as Question regarding rs.ViewDisplayMode and Is it possible to save rendered viewport image when current viewport is shaded? ?
Anyway, the way to go about this is to change the active viewport mode to what they want, capture it, then change back to whatever the display mode was.
Here a Python example to capture the active view
And to get a specific DisplayMode you can use
display_mode = Rhino.Display.DisplayModeDescription.FindByName("Wireframe")
and then set the view to use that with something along the lines of:
view = sc.doc.Views.ActiveView
view.ActiveViewport.DisplayMode = display_mode