That's correct. Under Download: Simulate ONTAP for ONTAP 8.x and 9.x, only 9.6 is listed. However, Simulators are upgradable, so that's a good news.
You will need to download the 'standard' ONTAP 9.7 image as we normally do from the support page (As you mentioned as well): You can simply go to bottom of download section where it says - "To access a specific version" and enter 9.7.
Once the image is in your repository, just follow the steps to upgrade the Ontap. I am sure there are notes on the upgrade steps on the forum as well on the google.
I found one example, user has upgraded from 9.6 to 9.7RC1, but at the moment, 9.7 GD is available to download.