Hope this code will helpful for you, the sku will be displayed at the end of shop loop
function shop_display_skus() {
global $product;
if ( $product->get_sku() ) {
echo '<div class="product-meta">SKU: ' . $product->get_sku() . '</div>';
}
}
add_action( 'woocommerce_after_shop_loop_item', 'shop_display_skus', 9 );