Processing Shipping with no cost

[lucillescandies]

I’m a small candy company just starting to take wholesale orders online. We have been in business for almost 100 years and this is our first time adventuring into the tech world. Prior to using an online web-based store we would take phone or email orders, process an electronic invoice and then accept payment via check cash or credit card over the phone.  Currently we use ship station as our shipping partner. We manually enter in each shipping option and pay for it ourselves, and then request it from the customer on the final invoice
For my new online store I have pickup, shipping and delivery options. So far the volume isn’t enough to integrate ship station and Shopify. My goal is to have our customers place orders and choose a delivery method. Since our shipping is not consistent (weight and package size) I would like to not charge the customer at the time of order. But instead charge them later when I found out the cost from ship station and add it to the bill at the end. Currently my store is processing payments via check and over the phone credit cards. And not accepting payments via Shopify. 
In Shopify when I go to shipping under settings I cannot have the shipping cost blank. If it’s zero dollars, then it says free. I basically just want them to be able to click shipping but not charge anything. Because it says free I feel like I’m going to give the wrong impression to my customers. Is there anything that I can be done or am I at a loss?