Last I heard, not shaving is a minhag and not halacha. Also, why can’t you hold your little daughter when you have a beard? What do people who never shave do then?
Sam, would that depend on what type of halel you say? I also heard quoted from Rav Schachter that only things that are specifically celebratory in relation to the day would be permitted, i.e. dancing, but not haircuts which we don’t generally do to celebrate.