Shipping billed later?

I make one off products and I don’t know the dimensions or the weight until after everything is packed up days or weeks later. I need to be able to bill people for shipping after the fact. I have it on the product description etc, but when the cart tells them it’s free they expect it to be free.

How do I do change this? If I leave the shipping blank the cart says free shipping. How can I make it read “shipping to be billed later” or something like that? I don’t want a shipping option or different services, I just want it to say, “you will be billed later.

Thanks in advance.