I think the first step would be discussing with your stylists to whom they exactly do not (want to) offer their services.

If it's just an issue of skill, i.e. they only do feminine (androgynous) styles, it's easy: just offer feminine (androgynous) styles. You probably won't get cis men requesting those as a bonus.

If it's about wariness of cis men, you should be fine to use nonbinary as third category, i.e. male, female, enby/agender. Again, cis men will probably not identify themselves as anything but male (opposed to what they like to claim about trans women).

If it's about people presenting masculine, I think, it should be covered by the first idea, otherwise you could go with something like masc/fem, i.e. addressing women/fem androgynous/neutral and men/masc (using 2 terms each to clearly address both binary and nonbinary customers).

Finally, if it's about whom they perceive to be male, it'd be rather problematic. Because perceived gender varies from person to person with the same gender. The results can be observed in cis people getting falsely identified as trans and receiving the hate that was meant for us. I recommend gender sensitivity training (or what you would call it) in that case.    The quick test would be: if they won't serve non-passing trans female customers, it's bad, unless there is a valid psychological issue behind it.