Disclaimer- I own Joss Whedon and therefore I also own the Firefly 'verse and all related characters by proxy. Don't believe me? Yeah, didn't think you would.
Inara cuts the hair on Serenity. Well, mostly.
She adamantly refuses to cut Jayne's hair unless he swears not to speak during. Even so it always takes place very quickly at the galley table. Jayne cleans up afterward. Inara believes the prostitutes Jayne frequents do it for him most times. She is unsure weither this speaks well or ill of him.
Mal's haircuts take place at the same table just as quickly. The only real difference between Mal and Jayne is that Inara always cuts Mal's hair and she does the cleaning up.
Zoë and River only ever ask for trims so Inara only ever cuts off the split ends and evens it up. It's really a shame. They both have such beautiful hair. Inara wouldn't lament the chance to play with it.
She also always cuts Kaylee's hair. She plays with it quite often.
Inara never cuts Wash's hair. She never means to conjure the image of him setting between his wife's knees as Zoë runs her fingers over his scalp.
Simon's haircuts always take place in Inara's shuttle amid talk and laughter. She can tell from his body language alone that he doesn't see her as a sexual or romantic partner. It puts her at ease.
Shepard Book never asks her to cut his and after sharing stories of Higgin's Moon she stops wondering why. He does let her braid it the night before she leaves.