User inputing manually the shipping value. Is it possible?

I’m shipping coffee mugs. They are very particular on prices, volume discount and shipping. Quite a nightmare. but I figure out how to deal with the fixed quantities and variable prices.
BUT!!!
the shipping I could not find an automated way to calculate the shipping, due to the amount of variables necessaries to get it.
So I’m thinking about something out of the box: The customer will be instructed to call me, and ask me for the final shipping price.
I will tell the customer how much it will be he he/she will fill a field that will add to the total price.

Is that possible? Any one saw it before?
I’m thinking in a way for the customer to complete the total price that his/her credit card will be charged…

Any ideas will be welcome.