Combine first 4 ingredients, stirring until well combined.
Trim crusts from bread; discard crusts. Spread each bread slice with about 1 1/2 teaspoons butter mixture. Place cucumber in a small bowl, and drizzle with lime juice; toss to coat. Arrange cucumber slices in an even layer over buttered sides of 6 bread slices; top with remaining bread slices, buttered side down. Cut sandwiches diagonally into quarters.