whatever smartphone, also with wake word, you wander around with these days
It's easy enough to disable the Android wake-word function. That does appear to prevent any visible reaction to it. Whether it prevents background recording is another question; hard to tell without rooting the phone and hooking some APIs, which is more effort than I'm going to go through right now.
Devices like the Echo, on the other hand, exist for precisely this purpose. For people who don't want "digital assistants" listening to them all the time, there's no reason to have one of the damned things.