How do I choose what default amount customers see in checkout for shipping fee?

When I go to the checkout page, it automatically shows the international fee which is the highest fee I charge, and that is before I enter any address details. If someone in the UK adds something to their cart, even though the price will be say £3 shipping, they will initially see £10 shipping and this might put them off buying. How do I change this? I would rather it say nothing at all until someone enters their shipping address.

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