My needle is about 2mm - I can't find my calipers to get a more accurate measurement, but I will bet that a needle 2.02 mm in diameter will work just fine. The needle is held by a screw down collet that should easily accommodate the extra width. My stitcher is a fairly old model and my not represent current production, like a great deal of my stuff. The needle is uniform diameter throughout, and isn't thicker at the butt end, like your illustration.
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Geezer in Chief