The short answer is maybe.
It sounds like your husband and his friends want to have an adult-child shoot. Other children near your sons age will be going with their parents. Sounds ok so far...
You don't say what rules went along with the Air soft gun or whether your son followed those rules, if he did he has proven himself to be responsible enough. If he has broken any of them or shown himself unsafe in any way, he has no business with a real gun.
I would hope that these adults would have some lower powered guns for the kids, ear protection, eye protection, etc... With the proper gear and protection, shooting is quite safe. If they don't have eye, ear and low-powered guns to shoot, say no! If they are going to a modern range, that helps too. A clearing in the woods... not so good.
As far as the sick feeling you get, your little boy is growing up. If you don't let him, he will be a warped little boy in a man's body. You married a Marine so I'm assuming you don't have an aversion to guns in general. Let your boy follow his father, it might be very healthy for him as he begins becoming a man.