Yes, you can use Wyze Cam v3 without Wi-Fi after setup.
Wyze Cam v3 is meant to work with an internet connection, which allows you to view the Live stream, get notifications, and change your camera settings in the Wyze app.
You must have an internet connection to set up the camera and configure it with the Wyze app. But if you have a microSD card inserted and Local recording to microSD card turned on in your settings, the camera will continuously record to that microSD card, even if offline.
To view your recorded footage, either bring your Wyze Cam v3 back to an area that is covered by the Wi-Fi network it was set up in and use the Playback feature in the Wyze app, or remove the microSD card from your Wyze Cam to view the raw video files (mp4 format) on a computer.
While the camera can do offline recording, it is not its optimal purpose.