The Wifi issue is separate from the internet connection issue - you could use a local Wifi network without there being an internet connection. You'd just have to set up a Wifi Access point which the cameras could all see.
If you want to view the cameras remotely while away from the farm, then obviously some sort of internet connection is required, but otherwise all systems should work if correctly configured, though hard wired one with POE are likely to be more reliable in my experience.
A Hikvision NVR would work fine and record to the hard drive for local viewing or later direct access (though best to hide the box somewhere to avoid any thieves taking it as well...)
A lot of the Wifi ones aimed at the domestic market do rely on cloud storage, and obviously those won't work without an internet connection - though some will record to a local Network storage if set up correctly.