Wa `alaykum as-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
1- It is not permissible for non-mahrams to shake hands with each other.
2- As for your situation, you can politely explain to your colleagues that you don’t shake hands with men; they should respect your attitude. Gradually, they would realize it and greet you without shaking hands.
3- From your part, you should show warm greetings and respect but without stretching hands for greeting.
Responding to your question, Dr. Muhammad Salama, PhD in Islamic Studies in English and Associate Professor at the Faculty of Islamic Science, Al-Madinah International University (Mediu), states:
Islam intends to build a community based on chastity, modesty and bashfulness. Therefore, Islamic teachings have laid restrictions on the interaction between marriageable men and women to block all ways to evil practices. Islam takes prohibitive measures and does not wait for evil to take place.
Women have been commanded to wear hijab, which is much more than a headscarf; it is a lifestyle and a way of conduct. Both men and women have been commanded to lower their gazes and not to look at members of the opposite sex except for a legitimate reason.
Moreover, unnecessary mingling between marriageable men and women is not permissible and any contact has to be within the Islamic guidelines in this regard. All evil practices between men and women are results of neglecting such teachings.
Even if there is no specific textual indication to the prohibition of shaking hands between non-mahram men and women, one will definitely infer that such practice is prohibited in Islam. If gazing at a woman is prohibited, touching a part of her body can never be permissible.
However, we have many textual indications to such prohibition. The Prophet (peace and blessings be upon him) refrained from shaking hands with women and said, “I do not shake hands with women.“(Ibn Majah) Though the Prophet was the most pious person and had the purest heart, this was not a justification for shaking hands.
In another prophetic narration authenticated by trustworthy scholars the Prophet (peace and blessings be upon him) warned, “Having his head stabbed with an iron needle is better for anyone of you than to touch a woman that is not lawful for him [to touch].” (Al-Bayhaqi and At-Tabarani)
Dear sister, you can inform your regular colleagues that you do not shake hands with men, and they should understand that as a personal attitude. But you should show respect and greet them with smiles or other gestures.
Allah Almighty knows best.