Drain the can of pink salmon and place the salmon in a medium bowl. (You may remove the skin and any small bones if you prefer, but it is not necessary.) Flake the salmon with a fork.
Crush 10 Saltine crackers (for the mixture) and set aside. Finely crush the remaining 15 Saltine crackers and spread those crumbs on a plate for coating. (To crush, place crackers in a resealable bag and crush with a rolling pin or pulse in a food processor.)
Add the 1/3 cup finely chopped onion, 1/3 cup mayonnaise, 1 teaspoon Tony Chachere's (or other Cajun/Creole seasoning or Old Bay), 1/2 teaspoon lemon zest, and the 10 crushed Saltine crackers to the bowl with the salmon. Stir until combined.
Taste the mixture and add salt and pepper as desired.
Stir in the 1 lightly beaten egg until the mixture is evenly combined.
Divide the mixture into 6 equal portions and form each into a patty. Dredge both sides of each patty in the plate of 15 finely crushed Saltine crumbs, pressing gently so the crumbs adhere. If time allows, refrigerate the coated patties for 30 minutes to help them hold together.
Heat 2 tablespoons vegetable oil and 1 tablespoon butter in a large skillet over medium heat until the butter has melted and starts to foam.
Cook the patties in the skillet, in batches if necessary, until golden brown on the first side (about 3–4 minutes), then flip and cook until golden on the second side and heated through (about 3–4 minutes more).
Transfer cooked patties to a paper-towel-lined plate to drain any excess oil and serve.