Place remaining ingredients into the bowl of a food processor. Pulse on and off until mixture is smooth but not pureed. Put mixture in plastic wrap and refrigerate until chilled, 1 to 2 hrs.
Place panko crumbs on a plate. Divide (4) equal size portions of shrimp mixture and roll them around on the crumbs to coat. Shape into thin patties.
Heat oil in skillet over medium-high heat. When oil is hot, fry cakes until golden brown and cakes spring back to the touch, (~ 2 mins per side). Drain on paper towels.