I believe there are different ways of achieving this. Simplest way I could imagine is as below:
$featured_content_query = new WP_Query( array(
'post_type' => 'feature',
'offset' => 1,
'posts_per_page' => 10,
'order' => 'ASC'
) );
shuffle( $featured_content_query ); //PHP function to randomise posts array
You can then continue to use $featured_content_query
as usual!