Hi,
What you could do is to set a "maximum price" in your shipping methods.
That way, no shipping method will be available over that amount and HikaShop will display an error message which you can customize with a translation override (to add a link to the contact form page for example), and it will prevent the customer from finishing his order.
Alternatively, you could let the user proceed, but with a "collect on delivery" payment method instead of your normal payment method. That way, you would be notified of the order, you could then add the shipping price to the order, and send an email to the user with a link to the payment form for the order. That way, it would be all automated, without having to handle phone calls.