How can I add a custom fee directly into shipping cost in woocommerce

I created a function to add a custom fee to the cart as insurance based on the amount spent only if the customer is shipping to the US and Canada. It works great. But I cannot figure out how to make it add this fee to the shipping amount instead of creating an additional line item.
Here’s the functioning code:

add_action( 'woocommerce_cart_calculate_fees', 'domestic_insurance_fee', 10, 1 );
function domestic_insurance_fee( $cart ) {

    if ( is_admin() && ! defined( 'DOING_AJAX' ) ) return;
    
        $cou = array( 'US', 'CA' );
                
    // The cart total
    $cart_total = $cart->cart_contents_total; 
if ($cart_total)
{
if ($cart_total >= 5000)
    $prc = 1.25;
    elseif ($cart_total >= 4200)
    $prc = 1.27;
      elseif ($cart_total >= 3200)
    $prc = 1.33;
      elseif ($cart_total >= 2200)
    $prc = 1.37;
      elseif ($cart_total >= 1600)
    $prc = 1.43;
      elseif ($cart_total >= 1100)
    $prc = 1.47;
      elseif ($cart_total >= 800)
    $prc = 1.55;
      elseif ($cart_total >= 600)
    $prc = 1.65;
      elseif ($cart_total >= 400)
    $prc = 1.75;
      elseif ($cart_total >= 200)
    $prc = 1.85;
      elseif ($cart_total >= 1)
    $prc = 2;
}
else
{
  $prc = 2;
}

    // The conditional Calculation
    $feess = $cart_total * $prc / 100 ;
     if ( in_array( WC()->customer->get_shipping_country(),  $cou, true ) ) {

        $cart->add_fee( __( "Insurance", "woocommerce" ), $feess, false );
} }

So I tried changing the last part that adds the fee to this:

    // The conditional Calculation
    $feess = $cart_total * $prc / 100 ;
    $ship_total = $cart->get_cart_shipping_total();
    $feeds = $ship_total + $feess;
     if ( in_array( WC()->customer->get_shipping_country(),  $cou, true ) ) {
$cart->set_shipping_total($feeds);
        
} }

But this does not work. Any suggestions?