You don't need to extrude it. Here is what I would do.
Partially cook and cool the shrimp in ice water. Set aside.
Cook grits fully and keep a little on the thick side.
Lay out a piece of butcher paper (by now, we all have some) or a paper bag, then out a layer of thick plastic wrap over it. Spread the semi-cooled grits onto the plastic in a ribbon about 2" in from one edge, place shrimp into grits.
Roll the plastic wrap, using the paper to assit in keeping it smooth, and wrap until all plastic wrap is tightly rolled. Grab ends and roll until sausage is formed.
Chill or ice bath until thickened. This is just like making compound butter but, thicker and with grits, cheese and shrimp.
I'm feeling bearish, and I'm packing a Wusthof Grand Brisket slicer from MABA
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