Make wings: In a medium bowl, whisk together lemon zest, salt, paprika, garlic powder, onion powder, thyme, and cayenne. Pat chicken wings dry and place in a large bowl. Add spice mixture and toss to coat.
Heat grill or grill pan to medium heat. Oil grill grates with vegetable oil. Add wings and cook, stirring occasionally, until skin is crisp and meat is cooked through, 15 to 20 minutes.
Meanwhile, make sauce: In a medium bowl, whisk together mayo, lemon juice, mustard, horseradish, chives, and hot sauce.