Putting this in the template file is the best I could come up with. However, now I’m not stoked that YouTube drops a cookie even from the no-cookie URL….
<?php
$iframe = get_field('video');
$iframe = str_replace('youtube.com/embed/', 'youtube-nocookie.com/embed/', $iframe);
?>
<div class="minus6db-video"><?php echo $iframe ?></div>