I have a workaround that I use for my UK clients who need to charge more for shipping to Scottish Highlands & Islands (for example) - it could be used for any region. You can use Product Variants to fudge the system. You can see an example and explanation of the steps here:
https://www.square-help.com/products/va-va-voom
P.S. @Beth_King You could create a Service product in a hidden page to charge the shipping for that person who bought without the shipping charge being added. Just set the price to be whatever the shipping was, and send them the link to pay (if you want to). Service products can be used to charge for anything - shipping, surcharges, deposits, whatever.