In the manipulator plugin screen there's nothing labeled 'hunter'. What's the name of the labor for hunting? "Ambusher"?
Ambusher is indeed the skill associated with the Hunting labor.
Just to confirm, images below using Manipulator and Dwarf Therapist. You can see that Udil's role is Hunter and they only have experience as in Ambushing. In both tools they have Hunting (H in manipulator) enabled. Both tools also list Ambushing as the actual skill.