Make external product's button on archives link to the product page.

functions.php

add_filter( 'woocommerce_loop_add_to_cart_link', 'wc_ninja_change_external_product_button', 15, 3 );
function wc_ninja_change_external_product_button( $button, $product, $args ) {
	$url = $product->add_to_cart_url();

	if ( 'external' === $product->get_type() ) {
		$url = $product->get_permalink();
	}

	return sprintf( '<a href="%s" data-quantity="%s" class="%s" %s>%s</a>',
		esc_url( $url ),
		esc_attr( isset( $args['quantity'] ) ? $args['quantity'] : 1 ),
		esc_attr( isset( $args['class'] ) ? $args['class'] : 'button' ),
		isset( $args['attributes'] ) ? wc_implode_html_attributes( $args['attributes'] ) : '',
		esc_html( $product->add_to_cart_text() )
	);
}

If you wanted to change the button text as well, could do something like this:

add_filter( 'woocommerce_loop_add_to_cart_link', 'wc_ninja_change_external_product_button', 15, 3 );
function wc_ninja_change_external_product_button( $button, $product, $args ) {
	$button_url  = $product->add_to_cart_url();
	$button_text = $product->add_to_cart_text();

	if ( 'external' === $product->get_type() ) {
		$button_url  = $product->get_permalink();
		$button_text = 'View Product Page';
	}

	return sprintf( '<a href="%s" data-quantity="%s" class="%s" %s>%s</a>',
		esc_url( $button_url ),
		esc_attr( isset( $args['quantity'] ) ? $args['quantity'] : 1 ),
		esc_attr( isset( $args['class'] ) ? $args['class'] : 'button' ),
		isset( $args['attributes'] ) ? wc_implode_html_attributes( $args['attributes'] ) : '',
		esc_html( $button_text )
	);
}