

Even “smaller” ships have a barber shop - for example the NS Savannah has one, and that has a max of 60 passengers and 124 crew. But they were expecting to be at sea for months at a time.
Voyager may have had a dedicated barber, or maybe someone learned to do it after they got stranded. Maybe they had an Emergency Barber Hologram!
“Please state the nature of the hair style emergency.”