Searchbar in top of shop page

Hi,

Question for woocommerce experts: I want to add a searchbar (I've created one with HTML) to the top of my shop page. Since there's no woocommerce shop shortcode, I can't just add my searchbar to the shop page and insert a shop shortcode below.
I've tried editing the products-archive.php file and it does display the searchbar, but it also messes up the rest of the page (plus other product-category pages).

Perhaps I'm inserting the HTML wrong in the php file? Unfortunately there's no widget area in my theme that allows me to add widget to the top of the page. Only to the sidebar.

Any suggestions?