This.
Management can make a decision only within the constraints of the law. Which gives them a choice of fully mixed sex, open to everyone; or single sex, provided it falls within the permitted single-sex exceptions. They can't pick and choose these men but not those men. All or none.
And the law uses the ordinary meaning of words unless specifically otherwise stated. Woman, female, lady, lass, damsel, whatever - you can't provide a service that illegally discriminates by using a synonym.