Combine the lemon juice, cumin, 2 tablespoons of the oil, ½ teaspoon salt, and ¼ 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, zest, ¾ teaspoon salt, and ½ teaspoon pepper. 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 tablespoon 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.