Magento – Magento 2: Adding Custom SKU for simple products in Configurable Product

Mapping the attribute options in the dropdowns to actual products can be done by using the spConfig javascript variable printed on the product view page of every configurable product.

var spConfig = new Product.Config({
"attributes":{
   "502":{
      "id":"502",
      "code":"shoe_size",
      "label":"Shoe Size",
      "options":[{
         "id":"46",
         "label":"3",
         "price":"0",
         "oldPrice":"0",
         "products":["32"]
      },{
         "id":"45",
         [...]
      }]
    }},
[...]});

Notice the products keys that have an array of product ids. Using some javascript that observes the onchange event of your option dropdowns you should be able to work your way through the array ending up with the product the user has chosen.

Now for mapping that to the product SKU, you're probably best of retrieving them from a custom javascript array which you can create by using the code from this article. So now for some untested code

$simple_collection = Mage::getModel('catalog/product_type_configurable')->setProduct(Mage::registry('current_product'))
                            ->getUsedProductCollection()
                            ->addAttributeToSelect('sku')
                            ->addFilterByRequiredOptions();

$id_to_sku = array();                           
foreach ($simple_collection  as $_item)
{
    $id_to_sku['p'+$_item->getId()] = $_item->getSku();
}   

echo '<script type="text/javascript">
var confIdToSku = '.json_encode($id_to_sku).';
</script>';

Which would output an array like

var confIdToSku = {"p32":"pr-sku-1", "p35":"pr-sku-2"}

That would enable you to map the product ID to the SKU you need.

I'd suggest creating a new PHTML file for this in your template directory, using block type core/template and calling that in the template/catalog/product/view.phtml.

I'm no hero with Javascript so I didn't include any javascript code examples in my answer, I hope you can figure that part out for yourself.