Lr

Lightroom Classic works fine if you do not have wifi. You only need to be online to install it, and then once a month so the software can check you still have a valid subscription.

Lightroom-Classic v11.2 works just exactly the same as your Lightroom v6 (perpetual) , with enhancements.

The only difference being that you need a subscription to the Photography Plan  (20GB) which uses a Desktop App (Adobe Creative Cloud Desktop App) to install Lightroom-Classic and manage your subscription and activation of LrC using internet access.

There is no Lightroom "CC". That designation disappeared quite a while ago. IF you are referring to Lightroom, the version that stores all your images in the cloud, that version can be used independently from Lightroom 6. The two versions are not compatible and cannot be used interchangeably. Work done in one version cannot be used in the other.

If you are referring to Lightroom Classic, I don't believe Lightroom 6 and Lightroom Classic can realistically coexist on the same computer. Even if they can, the catalogs are not compatible at all. In other words, you wouldn't be able to work on images in Lightroom Classic when Internet is available and revert to Lightroom 6 to continue the same editing process when the Internet isn't available.