Separate the egg yolks from the hard boiled eggs and place in a medium bowl. Add mayonnaise, vinegar, Worcestershire sauce, and paprika, and mash with a fork. Mix until smooth. Add more mayo if necessary for a smooth, creamy yolk mixture.
Finely dice egg whites and add to yolk mixture. Stir to combine. Add salt and pepper to taste.
Make two full sandwiches out of the egg salad. Then cut off the crusts and cut each sandwich into four fingers or triangles. If you cut them into fingers, you can tie a chive around each tea sandwich as a garnish. Sprinkle tops of sandwiches with paprika, if desired.
You can hard boil your eggs several days in advance. Egg salad can be made a day ahead and covered before assembling the sandwiches.