Adjusting Shipping Costs After Sale Made

I want to add a shipping method into my site that when selected will allow the customer to:

• - checkout and not pay straight away

• - then allow me to work out the exact cost of shipping

• - add it to the invoice

• - then send it to the customer to pay

The reason I want it is because my client uses a courier that charges by consignment. There is no way to work out how many items will fit in a consignment until it is all packed.

If there is another solution then I am all ears.