Remove update nags for non-admins [duplicate]

I’m trying to remove or hide the update nags for non-admin users. As an admin, I see:

The popular answer I’ve seen to handle this says to use:

function hide_update_nag() {
    if ( !current_user_can('update_core') ) {
        remove_action( 'admin_notices', 'update_nag', 3 );
    }
}
add_action( 'admin_head', 'hide_update_nag', 1 );

This works fine for removing the first message (WordPress 4.5.3 is available! Please update now) but leaves the second one visible to non-admins:

Both messages are wrapped in a <div class="update-nag">, so one option is to modify the above chunk of code to use CSS to hide the nag with:

echo '<style>.update-nag {display: none}</style>';

But this feels kludgy to me. Is there a way to hook into an action or filter and remove ALL the update nag messages for non-admin users? No third-party plugin recommendations please.

In wp-admin/includes/update.php file

if ( current_user_can('update_core') )
        $msg = sprintf( __('An automated WordPress update has failed to complete - <a href="https://wordpress.stackexchange.com/questions/231010/%s">please attempt the update again now</a>.'), 'update-core.php' );
    else
        $msg = __('An automated WordPress update has failed to complete! Please notify the site administrator.');

We can see that messages are different based on the current user role and this is maintenance_nag.

Basically we have two update nags and can be found in admin-filters.php

add_action( 'admin_notices', 'update_nag',      3  );
add_action( 'admin_notices', 'maintenance_nag', 10 );

So to remove second message we can use(also check for current user role if you want this only for non-admins)

remove_action( 'admin_notices', 'maintenance_nag', 10 );

For multi-site use

remove_action( 'network_admin_notices', 'maintenance_nag', 10 );