You would need to check them against something, like an array of field keys, for example:
// list of field keys to not show
$exclude = array('field_123', 'field_234', 'field_456');
// your loop
foreach( $fields as $field_name => $field ) {
if (in_array($field['key'], $exclude) {
// one of the fields to exclude
// skip it
continue;
}
// ..... the rest of your loop here ....