It depends on the elements you put in your div. However, anything you put in can be manipulated with sass/css.
If you for instance put a table in it with a element (button) per row, you could use something like this:
It is a basic example, but I hope it gives you a useful starting point. If you need more info on how to use/manipulate the 'hover' class, there is a lot of information online on the subject, as well as courses and code generators.
Hope it is of help!
It depends on how you're populating the div converter. If you use a list view then you can add a css/sass class to it which can give it your desired outcome. Can you upload a screen shot of the widget in the modeler?