How to add a custom class to all the images for a page only?

As long as your theme was created and coded properly each page has its own class already. Look at the body div in your code. You should see something like page-id-23. (the number is going to be different, as the number will be the actual ID of the page itself.)

So, all you have to do is use the selector .page-id-XX img

This will target all images on that page.