He is considering the possibility of using this invitation to present a prayer that expresses a sound, Scriptural view of faith, grace, and the Sacraments. In doing so, he hopes he would be able to provide a witness to these people. However, he is also very much aware of the Scriptural admonition to stay away from fellowship with individuals who subscribe to false teaching. Up until now, he has politely refused to lead the group in prayer. However, a majority of the men in our bible study this morning believed he should take the opportunity to lead a prayer and therefore witness to the retirees.
Prayer is always an act of worship.
Prayer is always a religious act. All prayer, therefore, should be offered in accordance with the biblical principles of fellowship, as you have noted in your question. Praying in the presence of a person is not the same as praying with a person. Simultaneous silent prayer within a group which is not united in doctrine is not an expression of prayer fellowship. Praying with a person, however, is always an act of joint worship and therefore an act of fellowship.