Place walleye fillets in a baking dish, pour in wine, and season with salt and pepper. Bake in the preheated oven until the fish flakes easily with a fork, about 20 minutes. Allow the fish to cool and break it into large chunks. Set aside.
Mix carrot, red onion, celery, panko crumbs, 2 cups mayonnaise, seafood seasoning, and 1 teaspoon salt in a bowl until well blended. Add the walleye, mixing gently so the chunks of fish don't break apart. Shape the mixture into 12 patties.
Heat vegetable oil in a large skillet or griddle over medium-high heat. Fry the patties until golden brown, 3 to 5 minutes per side.
Whisk lemon juice and fresh dill into 1 cup mayonnaise in a bowl. Drizzle the sauce over the walleye cakes and serve.
