I’m going to presume you’re not conducting illegal activity such that you’re worried about getting caught. Given that presumption, what risks are you trying to mitigate by treating your cell phone as you describe?
I think one way to circumvent this is to force all participants to keep the cellphones in their offices/homes, and then meet elsewhere at a predetermined time, with no one carrying phones.
As many security professionals often say, it's not about whether I do any illegal activity, it is also about whether someone can "impersonate" me for various crimes like phishing. The less sensitive information people know about you, the safer it is for you.