Add 2 tablespoons oil to a large skillet over meduim heat. Saute onion, celery and squash for 10 minutes until soft. Set aside to cool.
Drain the liquid from the salmon and crumble into a large mixing bowl, removing or crushing large bones. Add sauteed vegetables and remaining ingredients and combine thoroughly. Refrigerate for 10 minutes, up to 24 hours.
Preheat oven to 425 and prepare two large baking sheets with parchment paper brushed with oil. Scoop 1/4 cup of mixture, form into a ball and flatten slightly to make 12 cakes roughly 3 inches across by 1 inch thick. Brush the tops of the cakes with remaining oil. Bake for 30 minutes, flipping after 20 minutes.
Serve with tarter sauce, paleo mayonnaise or other sauce of choice.