https://ting.com/shop/alcatel-go-flip_Black-4GB-refurbished-...
I guess from the description that it does have some internet capabilities, but I would assume they can be disabled.
Another option if you're just trying to get away from Google/Apple would be an Android phone with Lineage OS and no Google services. You loose access to the usual Play store apps, but still have a lot more capabilities than a flip phone.
There is also microG, a free reimplementation of Google Play Services, which would allow you to even use apps that depend on that (for instance, for push notifications).
Of course what I actually recommend is doing neither of those and only using apps from F-Droid instead. But it is an option.
Obviously there's some inconvenience here, but it has the nice property that assuming you can use wifi at your main locations (home, work, coffee shop, library, etc), you'll only ever be on the cellular network in between places. And because the stick is naturally de-powered when not plugged in, there's no need to seek out a battery-removable phone.
Unless you're using the phone for a lot of calls and texting, it's probably not much worse to do it all from the "pocket computer" or laptop than to have two separate devices.
In any case, I traveled overseas ~12 years ago with no phone and just a white MacBook, so I'm aware of some of the compromises required, things like saving pages and making screenshots of maps, always on the lookout for places likely to have free or inexpensive wifi.
I haven't been able to find any real dumbphones that will work well in the US (non-LTE call service being phased out). Where are you and what do you plan to use?