In medium bowl, beat egg. Add all remaining patty ingredients; mix well. Shape mixture into 4 (3/4-inch-thick) patties.
Heat 12-inch nonstick skillet over medium-high heat until hot. Add patties; cook 6 to 8 minutes or until golden brown on both sides.
In small bowl, combine all sauce ingredients; mix well. Serve tuna patties with sauce and, if desired, additional pickle relish.