There is nothing wrong with a man greeting a non-Mahram woman with Salam, without shaking her hand, if she is elderly. However, he should not greet a young woman with Salam when there is no guarantee that there will be no Fitnah (temptation).

In countries where free mixing between men and women is widespread, a concession may be granted allowing the Muslims to study, teach, and work in mixed environments if they adhere to the Islamic rulings such as lowering the gaze, and not talking and engaging in conversation more than is necessary for the purpose of work or study.