Randomize Posts. Skip the first post in ascending order

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!