Preheat a grill to medium-high heat (375 to 450 degrees). Soak the wooden skewers (at least 20 minutes).
Pat the shrimp dry with a paper towel or clean towel. Place it in a bowl and add the olive oil, smoked paprika, garlic powder, onion powder, celery salt and kosher salt. Mix with your hands to combine.
Thread the shrimp onto the skewers, alternating direction of the tails and making the shrimp just touch each other (so they don’t spin when flipping the skewers).
Place skewers directly on the grill and grill 1 to 2 minutes per side, until bright pink and cooked through.
Remove from the grill and squeeze on fresh lemon juice from the lemon wedges. Top with finely chopped parsley if desired.