Display Day names with wp_get_archives instead of date

There are no arguments you can pass to do this, and no obvious filters. However, if you dig through the source you will see:

1426            if ( ! $archive_date_format_over_ride ) {
1427                    $archive_day_date_format = get_option( 'date_format' );
1428                    $archive_week_start_date_format = get_option( 'date_format' );
1429                    $archive_week_end_date_format = get_option( 'date_format' );
1430            }

That value is used here:

1514    $text = mysql2date( $archive_day_date_format, $date );

To create the “text” of the link.

It is possible to filter the output of get_option() 🙂

function hack_date_format_wpse_207803() {
  return 'l';
}
add_filter( 'pre_option_date_format','hack_date_format_wpse_207803' );
wp_get_archives('type=daily&show_post_count=1&cat=13703&limit=");
remove_filter( "pre_option_date_format','hack_date_format_wpse_207803' );

Your format= argument is preventing links. I removed that.