That's an entirely made up scenario.
No way would a GP's practice schedule a male nurse to do a routine cervical smear, pre booked in advance, because regardless of the patient's wishes, he would need to find a chaperone which would indeed be a waste of resources.
(The only time I've needed, on the basis of symptoms, to be given an unexpected internal by my then male GP, he went to get a chaperone before proceeding, as a routine thing.)
There are plenty of female nurses out there; practices know that scheduling a male practitioner would lead to endless complications and a need for chaperones. So they don't do it.
This only becomes a problem when genderist lobbyists press to make us all pretend that gender is a thing and that to be concerned by biological sex doesn't matter.