You may need to create a child theme to accomplish this. Personally, when I’ve done this type of thing in the past I’ve used a child theme with a php if statement or some javascript to print the html for the custom header on each page.
Hope this helps.
You should be able to use featured images to do what you want. If your theme does not already support featured images, create a child theme as Davood suggests. Enable featured images as discussed in the above link. Copy over to your child theme the header.php file of your parent theme and add something like
if (has_post_thumbnail()) the_post_thumbnail();
You will likely need to also set the featured image size. This is also discussed in the above link.
Hmmm. what bcworkz is suggesting actually seems correct if you are using on of the default themes. For many of the themes in the repository as well as almost all premium themes using featured images will not do what you are expecting and you will need to contact the themes developers for support.
