When you create a button element in Hype, it appears on the stage with three state options - normal, hover, and clicked.
You can choose from among those options and, in the element inspector, pick different styles for the button, including changing its fill color, its type … and its background image.
So that's how I'd probably approach this. Start with three separate images, one meant for 'normal' display, one for hovering, one for clicked. Then set those as the images in the button element in Hype.