How do I display a user’s previous orders as a select box option on a product?

You can try something like this:

add_action( 'woocommerce_before_add_to_cart_form', 'add_list_completed_orders' );
function add_list_completed_orders() {
    // get orders
    $orders = wc_get_orders (
        array (
            'status'        => array( 'wc-completed' ),
            'type'          => 'shop_order',
            'limit'         => -1,
            'return'        => 'ids',
            'customer_id'   => get_current_user_id(),
        )
    );

    if ( ! empty( $orders ) ) {
        // set value options
        $options="";
        foreach ( $orders as $order_id ) {
            $options .= '<option value="' . $order_id . '">' . $order_id . '</option>';
        }
        // add list
        $form = '<label for="orders">Select completed orders:</label>';
        $form .= '<select id="orders" name="orders">' . $options . '</select>';
        echo $form;
    }

}

Tested and it works. The code goes into your theme’s functions.php.