what do you mean by you can get into trouble for using a phone without a SIM card? A WiFi only phone is just a smaller tablet.
And yeah, cities with extensive camera vigilance can be a problem impossible to solve. There's not much you can do about that other than protest.
Your cell provider might track you via triangulation, but this is solved by either plane mode, turning your phone off or a Faraday bag. Of course those would render your phone useless (except plane mode and WiFi activated).
it's a problem quite difficult to solve right now. if you want a working phone, at least your cell provider will track you. But by using open street maps you don't give your data to Google too, so you minimize who has it.