How to save the field when updating the checkout?

Question

WooCommerce

I have a switch, radio type, with the value of which I want to filter delivery methods - if delivery is selected, then one, if pickup, then others.

$fields['shipping']['shipping_type'] = array(
    'required'  => true,
    'class'     => array(),
    'type'      => 'radio',
    'options'   => array(
      'flat_rate'  => 'Доставка',
      'local_pickup' => 'Самовывоз',
    ),
    'default'  => 'flat_rate'
  );

So, when the "update_checkout" event triggers, the indicator is always reset to default. Just don't save the value? Or it is necessary to do hands through session?