You could probably use the function get_header()
(https://codex.wordpress.org/Function_Reference/get_header) in combination with the page name ($pagename global WP variable), by doing something like this:
Apart from using the main - default header in header.php
, create your custom header PHP files following the name convention header-{name}.php
, in which you put your header specific code.
Then, in page.php
you can do:
get_header($pagename);
This will probably call the appropriate header based on your page name.