Heat a large skillet over medium-low to medium heat and melt the butter.
Add the bell pepper, celery and garlic. Cook between 3 and 5 minutes or until tender and fragrant. Add the garlic and the alligator meat to the pan. Cook for 3 to 5 minutes or until the alligator meat is fully cooked. Stir occasionally while cooking.
Remove the vegetable and alligator mixture from the pan and place it on a paper towel to absorb any access moisture. Place it in the refrigerator until thoroughly chilled. Keep in the refrigerator until step 7.
Place the raw shrimp and egg white into a food processor or blender.
Turn on the food processor or blender. While running, slowly pour in the heavy cream, kosher salt, and Cajun seasoning.
Puree the shrimp mixture until it is smooth. Place the pureed shrimp into a medium bowl.
Add the fresh herbs, along with the cooked and chilled alligator mixture to the bowl. Stir until fully combined using a spatula.
Stuff the mixture into the sausage casings and twist into around 4-inch links.
For best results, poach the links in water that is around 170 degrees F until you reach an internal temperature of 135 degrees F. Or you can steam the links if you'd like.
After the sausages are poached or steamed, I like to fry them in a cast iron pan with a little butter until the outside edges are lightly golden brown.