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 is His Slave and Messenger.
It is not permissible to be in seclusion with a non-Mahram woman. What is meant by seclusion is that a man and a woman become safe from anyone entering upon them. The Fiqh Encyclopedia reads: “It is not permissible for a woman to be in seclusion with a non-Mahram man even at work, and what is meant by seclusion is for a woman to be alone with a man and they are safe from a third person entering upon them.” For more benefit, please refer to Fatwa 88280.
On the other hand, marrying a Christian woman is permissible if she is chaste, but it is undesirable. However, it is permissible to resort to it in case of necessity, as in your case. Please refer to Fatwa 84159.
You are not obliged to inform your first wife or those who work with you about this marriage. Announcing the marriage is desirable but not an obligation, but it should fulfill the conditions for its validity, the most important of which are the consent of the bride's guardian and the presence of two witnesses as clarified in Fatwa 83629. It is her guardian from her religion who should marry her off, and if there is none, then a priest according to the view of some scholars or whoever may act on behalf of an Islamic judge according to the view of some other scholars. For more benefit, kindly refer to Fatwa 39267.
Finally, it should be noted that a condition for marrying more than one wife is to be just between them. There is no harm if the wife provides for herself and renounces her right upon her husband in this regard. However, it is not permissible to stipulate this as a condition in the marriage contract. If such a condition is stipulated in the contract, then this condition is void.
Allaah Knows best.