Is it permissible for a woman working in a mixed-gender environment to say "yarhamukallah" to a man if he sneezes?

Sneeze etiquette for a Muslim (tashmit al-'atis) is a communal obligation (fard kifa'i). The basis for this is the hadith (definition): "The rights of a Muslim upon another Muslim are six... and when he sneezes and praises Allah, then say 'yarhamukallah' (may Allah have mercy on you)." However, this obligation is conditioned on the presence or absence of fitna (temptation/strife). If there is fear of fitna from a man saying 'yarhamukallah' to a woman or vice-versa, then it is not permissible. For this reason, scholars differentiated between a young woman and an old woman, and between a mahram (definition) (unmarriageable kin) and a non-mahram woman. The point is that the issue revolves around the presence or absence of fitna. If no fitna is feared, then it is permissible for a woman to say 'yarhamukallah' to a man, and vice-versa.