CASE or other buid-in or custom function to change characters

Hello,
I was trying to code a small converter as in the title but based on my example the CASE works until the first condition is met only. So the question is whether there exists any SQL built-in function to perform such conversion? I saw (don’t remember the name of the function and where one can find it in the documentation in the internet) that SQL offers a good solution but seems MySQL doesn’t support it. Unfortunately REGEX also doesn’t support multicondition replacement. Please see the below code.

SELECT
	word,
	CASE
		WHEN word REGEXP "ę" = 1 THEN REGEXP_REPLACE (word, "ę", "e")
		WHEN word REGEXP "ó" = 1 THEN REGEXP_REPLACE (word, "ó", "o")
		WHEN word REGEXP "ą" = 1 THEN REGEXP_REPLACE (word, "ą", "a")
		WHEN word REGEXP "ś" = 1 THEN REGEXP_REPLACE (word, "ś", "s")
		WHEN word REGEXP "ł" = 1 THEN REGEXP_REPLACE (word, "ł", "l")
		WHEN word REGEXP "ż" = 1 THEN REGEXP_REPLACE (word, "ż", "z")
		WHEN word REGEXP "ź" = 1 THEN REGEXP_REPLACE (word, "ź", "z")
		WHEN word REGEXP "ć" = 1 THEN REGEXP_REPLACE (word, "ć", "c")
		WHEN word REGEXP "ń" = 1 THEN REGEXP_REPLACE (word, "ń", "n")
	END AS new_word
FROM words;