Combine the lemon juice, cumin, 2 tablespoons of the oil, 1/2 teaspoon salt, and 1/4 teaspoon pepper in a large bowl. Add the radishes and carrots and toss to combine; set aside.
Pulse the shrimp in a food processor until coarsely chopped. Add the jalapeño, orange zest, 3/4 teaspoon salt, and 1/2 teaspoon pepper and pulse to combine.
Place the flour in a shallow bowl. Shape the shrimp mixture into 8 patties and dredge in the flour, tapping off the excess.
Heat the remaining oil in a large skillet over medium heat. Cook the patties until golden brown and cooked through, about 2 minutes per side.
Divide the shrimp cakes among individual plates and serve with the carrot slaw, cilantro, and tortilla chips, if desired.
Make Ahead: The uncooked patties can be shaped (but not dredged in the flour), placed on a baking sheet in a single layer, covered, and then refrigerated for up to 24 hours or frozen for up to 3 months. Dredge the patties in the flour before cooking.