Is the shipping fee included in the customs value?

You should never change your product prices or shipping fees to meet under a customs threshold. This is illegal and is considered customs fraud. The customer is responsible for paying customs duties and if they do not want to pay for customs duties, then they should not purchase your product.

Your store policy should have a section that states how you handle customs fees. Our policy states that the customer is always responsible for the customs charges, no matter how big or small the purchase is.

That's what I thought. Just to clarify, would the shipping fee affect the customs duty?

The shipping fee is not typically included in the customs value. The customs value is usually only the value of the product.