For the salad: Cook the beans in a pot of boiling salted water until tender, about 3 minutes. Drain and plunge into a bowl of ice water. Drain again and transfer to a large salad bowl. Meanwhile, in a large saute pan over medium-high heat, heat the olive oil. Add the shallots, chile and garlic; cook, stirring, for about 1 minute. Add the corn and red and yellow bell peppers; cook, stirring occasionally, until the corn turns bright yellow. Remove from heat and stir in the lemon juice, chives and season with salt and pepper. Add the corn mixture to the beans and toss together well. Set aside.
Boil a large pot of salted water. Fill a large bowl half full with ice water. Blanch the green beans in the boiling water just until tender, 1 to 2 minutes. Remove with a slotted spoon and plunge into the ice water. Transfer to a large bowl. Add the corn to the boiling water and blanch until tender, about 3 minutes. Drain and let cool enough to cut the kernels off the cobs.
For the crab cakes: In a large bowl, whisk together the mayonnaise, mustard, hot sauce, Worcestershire sauce, egg yolks and lemon juice. Stir in the green onions, chives and parsley. Season the mixture well with salt and pepper. Fold in the crabmeat until coated thoroughly. Sprinkle the breadcrumbs over the mixture and gently mix together. Do not overwork the mixture. Carefully shape into 4 to 6 crab cakes.
Heat the oil in a large nonstick skillet over medium heat. When the oil is hot, add the crab cakes and cook until golden brown on the bottom, 3 to 4 minutes. Carefully flip the crab cakes and cook the other side until golden brown.
Toss the mixed greens with the bean salad and adjust the seasonings. Serve the crab cakes with the salad.