What you'd have to do is define your own field type in a module, then use hook_field_settings_form to set the global options for that field (or hook_instance_settings_form for a specific content type's implementation).
Here's a general guide to creating your own field in Drupal 7, but to get a handle specifics of creating a custom settings option take a look at other modules' implementations of it.
For example, Drupal Commerce makes a set of options from existing customer profiles:
function commerce_customer_field_settings_form($field, $instance, $has_data) {
$settings = $field['settings'];
$form = array();
if ($field['type'] == 'commerce_customer_profile_reference') {
$options = array();
// Build an options array of the customer profile types.
foreach (commerce_customer_profile_type_get_name() as $type => $name) {
$options[$type] = check_plain($name);
}
$form['profile_type'] = array(
'#type' => 'radios',
'#title' => t('Customer profile type that can be referenced'),
'#options' => $options,
'#default_value' => !empty($settings['profile_type']) ? $settings['profile_type'] : 'billing',
'#disabled' => $has_data,
);
}
return $form;
}
Yours sounds more simple - but the same general idea. Get the field and instance data, do something with it, make another mini form and return it so it gets rendered.