// This will take care of the Buy Product button below the external product on the Shop page.
 add_filter( 'woocommerce_loop_add_to_cart_link',  'ts_external_add_product_link' , 10, 2 );

  // Remove the default WooCommerce external product Buy Product button on the individual Product page.
 remove_action( 'woocommerce_external_add_to_cart', 'woocommerce_external_add_to_cart', 30 );

  // Add the open in a new browser tab WooCommerce external product Buy Product button.
 add_action( 'woocommerce_external_add_to_cart', 'ts_external_add_to_cart', 30 );

 
function ts_external_add_product_link( $link ) {
          global $product;

          if ( $product->is_type( 'external' ) ) {

                    $link = sprintf( '<a rel="nofollow" href="%s" data-quantity="%s" data-product_id="%s" data-product_sku="%s" class="%s" target="_blank">%s</a>',
                    esc_url($product->add_to_cart_url() ),
                    esc_attr( isset( $quantity ) ? $quantity : 1 ),
                    esc_attr( $product->id ),
                    esc_attr( $product->get_sku() ),
                    esc_attr( isset( $class ) ? $class : 'button product_type_external' ),
                    esc_html( $product->add_to_cart_text() )
                    );
          }

          return $link;
 }

function ts_external_add_to_cart() {
                    global $product;

                    if ( ! $product->add_to_cart_url() ) {
                    return;
                    }

                    $product_url = $product->add_to_cart_url();
                    $button_text = $product->single_add_to_cart_text();

/**
 *  The code below outputs the edited button with target="_blank" added to the html markup.
 */
                    do_action( 'woocommerce_before_add_to_cart_button' ); ?>

                    <p class="cart">
                    <a href="<?php echo esc_url($product_url); ?>" rel="nofollow" class="single_add_to_cart_button                                                           button alt" target="_blank">  
                    <?php echo esc_html($button_text ); ?></a>
                    </p>

                    <?php do_action( 'woocommerce_after_add_to_cart_button' );

 }