I would like additional function in js that adds an additional class 'ajax-register' to the modal's tag 'div.ctools-modal-content' when clicking on some of the links in the ajax-register block ('ul.ajax-register-links li a'). Doing that we could style the ajax-register's modal window for ajax-register only.

Something like

jQuery(document).on( "click", "ul.ajax-register-links li a", function()
setTimeout( "jQuery('div.ctools-modal-content').addClass('ajax-register');",50 );
});

but in a better drupalish way.