There’s a long discussion about soft lenses in ????? ??? ??? ?”?, ???? ?”? and ‘?, and in the ‘?????? ????, ??? ?.
Not only is it not a chassid shoteh question, he quotes R’ Elyashiv, R’ Vosner, and yl”t R’ Karelitz as all assering using cleaning solution.
Plain sterile water or saline solution, with no added cleaning agent, is okay if the lenses were clean before Shabbos.
??”? ??? ?”? ?’ ?”? allows soaking soft lenses to prevent them from getting ruined, and doesn’t mention cleaning solution.