Slice boiled eggs in half lengthwise. Scoop yolks into a bowl.
Mash yolks with a fork. Mix in mayonnaise, Dijon, hot sauce, sugar, and 1 teaspoon Cajun seasoning until smooth. Chill filling for 1–2 hours.
Season shrimp with 1 tablespoon Cajun seasoning. Heat olive oil in skillet. Cook shrimp 2 minutes per side, until pink and cooked through. Let cool.
Pipe yolk mixture into egg white halves using a piping bag or Ziploc with corner cut.
Top each egg with one shrimp, a slice of jalapeño, and a sprinkle of fresh chives.
Arrange on platter with lemon wedges. Serve immediately or chill for up to 2 hours.