Drain shrimp. Boil eggs; cool, peel, and chop. In a separate bowl, beat cream cheese, mayonnaise, mustard, horseradish, salt, and ketchup. Take onions and chop white and green sections. Lightly fold in onions, eggs, and shrimp into cream cheese mixture. Mixture should not be runny.
Spread mixture on slices of rye cocktail bread. If you want, you many put a lettuce leave beneath the mixture. You can also make decorative shapes with the bread by cutting with a cookie cutter.