I'm thinking of suggesting to my wife that we hire someone to do our daughters' hair while she's away
What is wrong with you doing her hair?
Nothing is wrong with that. I was thinking of hiring a better person.
Even though another person might do a better job, as a parent it is good to do your share for your child. You cannot expect your wife to do everything, it could cause resentment in your marriage.
There are just some things I don't want to do.
Of course, no one likes to do the bad or ugly jobs, but they need to get done. Being parents means that both of you have to contribute to the welfare of the child equally.