The correct answer is option 1, Holothuria. A notochord is a flexible and supportive structure found in certain chordate animals. It serves as a precursor to the spine and is present during the embryonic stage.

Option 2, Herdmania, is a type of ascidian or sea squirt. Ascidians are marine invertebrates and possess a notochord during their larval stage, but it disappears as they develop into adults. Therefore, they do possess a notochord at some point in their life cycle.

Option 3, Exocoetus, refers to a genus of flying fish. Flying fish are also chordates and possess a notochord during their embryonic stage. As they grow and develop, the notochord is replaced by the vertebral column or spine.

Option 4, Salamander, is an amphibian and a chordate. Salamanders possess a notochord during their embryonic stage. However, upon reaching adulthood, they retain their notochord to some extent in addition to having a vertebral column.

Therefore, the only correct answer is option 1, Holothuria, as it does not possess a notochord at any stage of its life cycle.