First off, hello and I have had my own reservations about first experiences in swinging. I could go out on a limb and say that many other couples/people have had concerns about there first time as well. I have found that when you are at the actual moment of swapping, that personal insecurities, ie size, body type, etc goes out the window. Especially when you are desired by another human being. I know a lot of people are going to disagree with me but, in my experience that is what happens. Please note that this is from a guys point of view.
I recall one experience when a couple and us were all in the same room and it was awkward for all of us. That sense of being “watched” by your SO is sometimes overwhelming. From that point forward we would split off into separate rooms. If you all are ok with separate rooms, I would try that. In my opinion that is a much less stressful situation but it does warrant rock solid trust between you and your husband.
Hope this helps.