I would just say it like its normal and then wait for their reaction.
You have to realize one thing…what-to-do and what-not-to-do is set by society and society is made up of people like you and I. If you wear bell bottoms with confidence, no one will question you. I once worked with a woman who wore BRIGHT YELLOW BOOTIES and because she loved them…so did everyone else. And even though I thought they were positively hideous, I found myself trying to find something to like about them.
Its an over simplified example Im giving to illustrate my point. Islam allows cousin marriages and thats the bottom line. Your job is to make sure you understand the reasoning behind it and present it in a way where people get it. You should NOT hide it. That means you’re ashamed…you’re not ashamed…right? You love your husband? You want to be happy with him…make sure you’re ready for blows like these from non-muslims. Besides, these people are only in your life for as long as you have this job…he is your husband for life…Inshallah.