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The shifter body should be on the inside of the panel. Only the shifter and a keyed shaft should go through the panel itself. The only other thing is the cover plate. You should be able to remove the shifter handle, then remove the cover plate.
The cables only go to the inside shifter 'body', not through the panel itself. Whether the shifter mechanism is mounted to the panel as well, or whether the panel is cosmetic is another story.