Adding the attribute "inert" to the image prevents Edge showing the button completely but the image still displays and prints. You can wrap this with an link and a to get images to work as links.

<a href="www.bing.com" target="_top">
  <div>
    <img inert src="https://cdn.sstatic.net/Sites/stackoverflow/Img/apple-touch-icon.png">
  </div>
</a>