RE: I wanted to ask, can this be done using Contact Form 7
Yes - if you have suitable skills & experience
RE: Can I just add javascript to my header
This is considering very poor practice in WordPress - see http://www.wpbeginner.com/wp-tutorials/how-to-properly-add-javascripts-and-styles-in-wordpress/
RE: If I have to add a hook in the plugin what is the best place to do it so subsequent updates to the plugin don't break my changes.
Do in functions.php in Child Theme if mod will only be used in current theme. If you want to port this functionality elsewhere consider adding your hook in a small extra plugin.