Instead of doing the query to get a list of all avialble fields, construct an array with the field that you want to search.
$fields = array(
'field_1',
'field_2',
'field_3',
'field_4',
'etc...'
);
then alter the code used to display the field to use this new array
foreach ($fields as $field) {
printf('<option value="%s"%s>%s</option>', $field, $field == $current? ' selected="selected"':'', $field);
}