Hi,
Then I would still recommend to develop a small shipping plugin based on the manual shipping plugin and implement the onShippingDisplay function to set the price of the shipping methods dynamically based on the custom item fields values of the products in the cart.
That's for the checkout. For the product page, if you want to display a shipping value after the user selects stuff in the custom fields, you would have to add custom javascript to the file "show_block_custom_item" via the menu Display>Views.