In a bowl, mix the crab, shrimp, cucumber, mayonnaise, and parsley. Season with salt, and pepper. Cover, and chill until serving.
Slice the avocados lengthwise, and remove the pit. Scoop out the flesh of the avocado, leaving about 1/2 inch on the peel. Spoon the seafood mixture into the hollowed centers of the avocado halves. Sprinkle the tops with paprika.