There's nothing about the Shapechanger subtype that prevents them from being vulnerable to Hold Person, Charm Person, Dominate Person, or any other Compulsion based Mind-affecting spells.
You may be confusing Shapechanger's ability to override Polymorph effects with their own transformations with mindless creatures and their immunity to Mind-affecting spells.
Natural Lycanthropes don't have immunity to Mind-affecting spells either, so the answer is the same for either of them. Unless the creature already possesses a subtype that makes them immune to Mind-affecting spells, Charm Person, Hold person, etc. work as normal.