Because the pages in the new version doesn't need to be edited (hard-coded), it seems better to use PO/MO directly for the multi-lingual website.

language-detector.php

<?php
/**
 * Language detector
 * This global variable is used to detect the language that the user's browser is using.
 * Should be passed to step to get the specified language's MO file.
 */

function applemint_locale( $locale ) {
  //Create a global variable so that other functions and hooks can use the variable to determine the language.  
	global $am_lang;
  //Set up default lanuages that can be matched.
	$locale_list = array(
		'zh'         => 'zh_TW',
		'zh-hant'    => 'zh_TW',
		'ja'         => 'ja',
	);
  //Detecting the language either with the GET variable `lang` or the browsers' default.
	if ( isset( $_GET['lang'] ) || isset( $_SERVER['HTTP_ACCEPT_LANGUAGE'] )) {
		$am_lang = $_GET['lang'] ?: substr( $_SERVER['HTTP_ACCEPT_LANGUAGE'], 0, 2 );
	} else {
		$am_lang = 'ja';
	}
  //Matching the locale.
	if ( array_key_exists( $am_lang, $locale_list ) ) {
		$locale = $locale_list[$am_lang];
	} else {
		$locale = 'ja';
	}
	return $locale;
}
add_filter( 'locale', 'applemint_locale', 20, 1 );

/**
 * Language attributes transformation
 * This is used to set up the correct zh-hant language attribute rather than zh-TW.
 */
function applemint_lang_attr( $output, $doctype ) {
	global $am_lang;
	if ( preg_match( '/^zh/', $am_lang ) ){
		$output = preg_replace( '/lang="([\w-]+)"/', 'lang="zh-hant"', $output );
	} else {
		$output = preg_replace( '/lang="([\w-]+)"/', 'lang="' . $am_lang . '"', $output ); 
	}
	return $output;
}
add_filter( 'language_attributes', 'applemint_lang_attr', 21, 2 );