Customize custom-header

Hello kindly internet,

I would like to modify custom-header.php so that a user can input a URL that the custom-header image will link to.
e.g. <a href="<?php echo my_user_inputted_url(); ?>"><img src="<?php header_image(); ?>" height="<?php echo get_custom_header()->height; ?>" width="<?php echo get_custom_header()->width; ?>"/></a>

Ideally, the user would be able to choose a page created in wordpress from a dropdown list of currently published pages and the link for that page would be added to the header banner.

Alternatively, it would just be a text field with the URL that the user pastes, echoed into tags around the custom-header.

I don’t know how to do that through functions.php in my theme. Is it possible to hook into it and not touch the core files?

The twenty-ten, twenty-eleven themes have some customization of the custom-header.php admin screen but I don’t know how to customize it in the way I want.

Please help

Louise