Why would your secularism turn you into fashion police?
Why cannot a person wear a headscarf (it does not obscure their mouth or eyes so does not inhibit communication) if they want to? For what ever private reason they feel they want to?
I know people who wear them for non-religious reasons. Will they be exempt from your rules about fashion?
People get told all the time that what they wear is unacceptable by others in power, and it is an abuse of power. This is particularly true for women and a "headscarf" ban another example of blatant misogyny.
What is particularly offensive is it is said it is one for "liberating" those women. Often (usually not always) it is non Islamic people lecturing Islamists.
The fight against misogyny in Islam is a fight for Islamic women. When there is a cry from Islamic women for non-Islamists to set fashion laws for Islamic women to obey (and not just the odd lone voice) then maybe, possible you might have a point. Is that ever going to happen?
I do not think that Islamic women need misogynist, sexist, Islamophobic, theophobic, bigoted, and patronising rules and punishment. To liberate them, no less! Perhaps they need the opposite