Hi!
Actually, you can completely turn off the stylesheet loading via a small custom code snippet, when using the latest version of the plugin (4.19.4).
Try adding this custom code to the functions.php in your theme/child theme directory. Before editing, please make sure to have a full site back-up just in case!
add_filter( 'asp_load_css', 'asp_stop_load_css', 10, 1 );
function asp_stop_load_css( $stop ) {
return true;
}This will fully remove the search styling files, so you can build your own set of CSS rules instead. I hope this helps!