Looks like that message is the default message shown when no shipping rates are available. I agree that it is not as helpful as letting them know “The minimum order for shipping to the UK is 10”.
I am not sure that Shopify Scripts can help in this case, but perhaps you could do one of the following:
1. Adjust the messaging using Shopify’s internal language tool
Go to Admin > Settings > Checkout
Click the “Manage checkout language” button
Find the default messages you want to change (Try search the page for “offer shipping to”)
Update those messages to be more accurate to your store’s policies