For the aioli: Melt the butter in a small nonstick skillet over medium heat. Cook, stirring, until the shallot is just soft, about 3 minutes. Allow to cool.
Combine the mayonnaise, chives, lemon juice, dry mustard and shallots in a small bowl. Season with salt and pepper and let sit for about 10 minutes for the flavors to blend.
For the crab cakes: Mix together the crabmeat, crushed crackers, corn, bell pepper, mayonnaise, chives, mustard, Worcestershire, egg and lemon juice in a large bowl. Season with salt and pepper. Shape into four 1-inch-thick patties and dust with flour.
Heat up a couple tablespoons of oil in a medium nonstick skillet over medium heat. When the oil begins to give off just a hint of steam, carefully place the patties in the skillet and fry until golden brown, 4 to 5 minutes per side. Serve the cakes with the aioli. Enjoy!