Hi Ewan,
To do that, you’ll need to create your own close button image and then override the style rule that controls that close button image. I’d suggest to start with a copy of wp-content/plugins/easy-fancybox/fancybox/fancybox.png and change/replace the parts of the image that you want to see differently. Close button and matching left/right arrows for example… Then upload the new file to your site and add a rule like this to your themes stylesheet.
#fancybox-close {
background-image: url('/wp-content/uploads/2015/07/fancybox.png') !important
}
You could also use Jetpack’s Custom CSS module to append this rule. Note that the URL there depends on your modified image name & location of course.