Is the pilgrim permitted to shorten the hair of his head himself after 'Umrah, or is he required to ask someone else who has exited ihram to do that?

"Exiting the state of ritual consecration (for Hajj or Umrah (definition)) is done by shaving or shortening the hair. It is preferable for the pilgrim to ask someone else to shave his hair, as the Prophet, peace and blessings be upon him, did, to ensure that the entire head is shaved. It is permissible for the pilgrim to shave his own hair, and it does not affect the ruling whether the shaver is in a state of ritual consecration or not."