You can order it as separate app, but that's 19.95 /mo annual commitment
Go with the Photography Plan anyway. You are not obligated to download the Lightroom CC until you are sure it won't be a problem.
The Photography Plan includes PS Extended and latest LR but you're under no obligation to download & install LR until you're ready. My guess is you will want it because it has new features the old one doesn't.
You can have multiple versions of products on your system. That's no problem because they install to separate folders.
While it is possible to subscribe to Photoshop only, you probably don't want to - it's twice as expensive as the Photography Plan.
So I would recommend subscribing to the Photography plan, which will also give you more features in Lightroom than LR6 (like Dehaze, Guided upright, etc).
You should be able to convert your existing LR6 into LR CC - it's the same install, the only difference is in the licensing.
But to be on the safe side, I would uninstall LR6 (don't worry, it will not remove your catalog/edits or your photos), then install the CC desktop app, and use that to install Photoshop and Lightroom CC.
LR CC should find your LR6 catalog, if it doesn't, just point it to the catalog.