Careful the Ron Paul folks will tell you that the state has no authority
You get sick? Sue the owners
This isn’t about all or even chiefly health education.
If it’s about health, the government could also pass out information sheets to the public to watch for, i.e. does your cosmetologist do thus and such, and why she should. Nobody wants to pass around disease carelessly, but somehow we can’t all be bubble boys either. Sane vigilance should be the rule, and matters of artistry not under government purview.
I always think of libertarians as people who have, till now, not been sick and helpless . . . and very grateful for someones kindness.