Hey Melanie,
You should be able to by overriding the content-no-results.php file on your child theme. Simply change the get_search_form function there with the new function you want. Give it a shot and let us know how it goes! 
Ben
Hey Melanie,
You should be able to by overriding the content-no-results.php file on your child theme. Simply change the get_search_form function there with the new function you want. Give it a shot and let us know how it goes!
Ben