Nick here from Shopify.
This is something which would be quite customized in terms of the shipping settings and not native to the Shopify admin, which only allows setting prices by weight or price percentage now as you mentioned. Your best bet in this instance would be to use an app from the app store. A custom job from a developer could be costly. Let's take a look at some of the best possible app solutions below:
Don't hesitate should you have any other questions.
All the best, Nick