>I might be hoping to arrange a meeting or I might just be making conversation. 「打ち合わせをしたいのですが、四時はいかがでしょうか？」 「打ち合わせをしたいのですが、四時のご予定はいかがでしょうか？」 "四時になにをしていますか" sounds like "What are you doing at 4?". It is a little abrupt and people might get upset/confused. *However, if you speak it gently, they would understand your intention.

Thanks for your response. Does it work in either situation? I might be hoping to arrange a meeting or I might just be making conversation.

I want to understand the context. What's your intention of this question? Do you want to know if they are available at four or not, or you just want to know the thing they will be doing at 4?