Hi!
Most likely the best way to do this is by disabling the code, that is responsible for the stylesheet addition.
Open up the wp-content/plugins/ajax-search-pro/includes/shortcodes.php file. On the line 50 you should see this:
add_action('wp_print_styles', 'search_stylesheets');
Comment out that line, and the complete styling should disappear:
//add_action('wp_print_styles', 'search_stylesheets');