Buy a camera. And/or an audio recorder. Or pull the SIM out of an old phone and use that.
I'm no expert on cell networks but my impression is the baseband will still ping towers and participate in the cell network on some level. If the phone gets confiscated or its IMEI otherwise associated with you, it can probably be abused to try place you in an area at a given time even without the SIM card.
Just use cameras without any RF hardware. (they tend to have better optics / zoom capabilities anyways)
It's insane if you think about it but the phone company knows as much or more about you than your mother or your spouse.