Is it permissible to work as an anesthetist in cosmetic surgeries—such as liposuction—knowing that the nature of the work does not require uncovering the 'awrah, and refusing to do so may lead to dismissal from the job?

Cosmetic procedures are divided into two types: The first is permissible, and it is for removing a congenital defect or one resulting from an accident, or for removing harm, such as removing excessive obesity. As for the second type, it is forbidden, and it is for excessive beautification and not for removing a defect or harm. The Prophet, peace and blessings be upon him, cursed those who do that, because it is a change to Allah's creation. Based on this, if the procedures are permissible, there is no harm in participating in them while lowering one's gaze. If they are forbidden, participation in them is not permissible because it is assisting in sin. If your refusal to participate leads to dismissal, and you can do without the job, then it is obligatory not to comply with what is forbidden. If you are compelled and have no other means, then there is no objection to complying until another means becomes available.