Can I take customer order without processing payment till after a manually calculated shipping charge

You can use a Purchase order payment field on your form. This acts as an order form but does not require payment via the field.

Here is a useful guide: https://www.jotform.com/help/460-how-to-create-payment-form-with-purchase-order

After getting the order, you can then charge the customer manually after adding the required shipping charge.

Would this help?