Preheat the oven to 325 degrees F (165 degrees C). Generously butter a loaf pan.
Melt butter over medium heat in a saute pan until bubbling. Toss in onion, give the pan a quick shake, and stir with a wooden spoon; cook for 1 minute. Turn off the heat and allow to cool.
Place salmon in a large mixing bowl and mash with a fork. Add cracker crumbs, salt, cayenne pepper, Worcestershire sauce, rice vinegar, butter, and onions; mix and mash with a spatula or spoon until smooth.
Separate eggs, adding whites to a clean glass, metal, or ceramic bowl and adding yolks to salmon mixture. Mix egg yolks and salmon until well combined.
Whisk whites to medium stiff peaks. Gently fold into salmon mixture in 2 additions.
Transfer salmon mixture into the prepared loaf pan. Smooth the top with a spatula to even it out and shake and tap the pan to remove any air bubbles.
Bake in the center of the preheated oven until a toothpick comes out clean, about 45 minutes. Let rest for 5 minutes, then carefully turn loaf out onto a cutting board. Slice and serve.