You can by overriding the standard given classes for that dialog, but that would then inflect to all the elements that use these classes through your app. I personally would advise against it.
You will be more flexible when you call a new pop-up page with a cancel and leave button and create the logic yourself. With a custom page, the option to style it so that it fits your needs is easier, and it also won't reflect your whole application as you can use custom classes.
Hope this helps.
Yes, we can change any default UI by overriding its styles, targeting the proper class names.