Hi,
You should be able to do that by default with HikaShop.
You just need to enter the value you want in the "maximum price" setting of your existing shipping methods, and create a new manual shipping plugin instance with a price of 0 and a "minimum price" with that same value.
That way, when the cart total amount is below that value, you'll see your existing shipping methods, and when it is above, you'll see that manual shipping method with a price of 0 which will actually show "free shipping" instead of the price.