I'm too old to worry about embarrassing myself. Bring it on.
I was never really intimidated by instructors even in high school. Since I went to a private Catholic school we couldn't speak until called upon. I seriously had no problem with saying "I have no idea, sorry." They would try to make you look stupid, but I had every right to answer back without being disrespectful, thus, ultamately earning the respect of my teachers. College was a joke, as an older guy, all the younger people thought I knew everything, and I knew less than them. Even after I showed them my grades, they still thought I was a better student. Very strange.
I bring this up because in UGRAD almost all of my classes adjusted grades, or had the ability to adjust grades 10%, for so called class participation. I think it's more ass kissing, but as an older student, they just want your respect, so I gave it to them.
I really can't see the problem worrying about being called on. "I don't know, I have no excuse, it will never happen again." Any other BS thrown at you, let two words be your friend "I'm sorry." Say it every time s/he continues to try to make an ass out of you.
Sooner or later, the ass is exposed.