Mix water and blue food color in a large bowl. Crack the shells of the hard boiled eggs gently with a spoon. Do not remove the shell. Put the cracked eggs in the water and food coloring mixture and refrigerate for at least 2 hours. Remove eggs from the refrigerator, peel carefully, and cut eggs in half lengthwise. Scoop out the egg yolks and transfer to a bowl. Set the whites aside. Mash the yolks with the mayonnaise, green food coloring, mustard, and vinegar and pipe the yolk mixture into the egg whites. Garnish with black sesame seeds.