All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
It is not permissible for the Muslim woman to work in a job that involves violations of Sharee'ah such as being alone with non-Mahram men and shaking hands with them. Such matters are prohibited. For more benefit, please refer to Fataawa 82112 and 133843.
If there is no way to avoid such prohibited matters in that job, then it is not permissible to work in it. The circumstances that you have mentioned do not make this job permissible for it is not included in the necessities that make forbidden things permissible. Scholars have defined necessity as what would most likely cause one to fall into unbearable hardship if he/she does not do the prohibited matter. Maybe if you fear Allaah The Almighty, He The Exalted will make for you a way out of difficulty and make easy for you His ways of provision. Allaah The Almighty says (what means): {And whoever fears Allaah - He will make for him a way out And will provide for him from where he does not expect.}[Quran 65:2-3]
It was authentically narrated that the Prophet, sallallaahu ‘alayhi wa sallam, said: "You will never give up something for the sake of Allaah, may He be glorified and exalted, but Allaah will replace it with something that is better for you than it." [Ahmad]
For more benefit, kindly refer to Fatwa 82399.
It is worth noting here that it is not permissible for the Muslim individual to compromise in religion out of courtesy with any person, for religion is the most precious and the pleasure of Allaah The Almighty is the most sublime thing. Allaah The Almighty says (what means): {They wish that you would soften [in your position], so they would soften [toward you].}[Quran 68:9]
Also, it was narrated that ‘Aa’ishah said: “I heard the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, saying: "Whoever seeks the pleasure of Allaah by angering people, Allaah will suffice him against the people, and whoever seeks people's contentment by angering Allaah, Allaah will forsake him and leave his matters to the people." [At-Tirmithi]
Allaah Knows best.