While editing a publish that consists of a picture, Wordpress attaches a qualities inspector icon within the image to permit editing fundamental qualities for example size, alignment, link etc.

Let me understand how difficult it might be to compromise into this dialog screen and then add custom programming towards the link area.

Let me give a popup menu there will be able to access using the mouse click (near the existing "Connect to Image" button.

I'd would rather hook into this dialog using a file during my theme's folder or using a plug-in. I'd rather not affect the wordpress code itself (to permit this to become more portable and theme specific).

The edit image popup is really a TinyMCE wordpress plugin (the wealthy text editor that Wordpress uses), the files that have been in wp-includes/js/tinymce/plugins/wpeditimage/.

As a result you cannot simply employ the Wordpress wordpress plugin API to change it. You'd have to make your own TinyMCE wordpress plugin, most likely by copying the wpeditimage wordpress plugin and adding your extra functionality. You'd should also produce a Wordpress wordpress plugin to activate the TinyMCE wordpress plugin, see these codex pages for additional info on dealing with TinyMCE plug ins in Wordpress: