Billing shipping separately?

I am setting up my website and need to decide on the shipping modules. After talking with the courier services, it is clearly just too complex to do online. I would like to have the customer pay for the cost of the item/s and then I will send them a PayPal invoice for the exact cost of shipping/insurance once the package is packed.

Is there a module for this?

You'd have to use something like the Store Pickup module, and simply change the text to say something about the idea that you'll bill them for shipping later.
But, it would show as $0.00 on the order, next to those comments, so be sure to explain that.

You'd have to do your PayPal billing entirely separately from Zen Cart, and manage all of that manually on your own.