Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Working in such a speciality should be limited to women, unless there is dire necessity in a given country for this speciality and if there are no women who could do the job as mentioned in the question. But men working in such a field should act within the limits of Shariah.
So, if those who carry out this job are unskilled non-Muslim workers, then it would be better that a good Muslim man carries out this mission but not exceeding the minimum necessary.
Finally, there should be a real endeavour to train Muslim women to do this job.
Allah knows best.