For me not even deleting the entire ~/.Skype directory works.
I've disabled the chat history in the options, quit Skype, deleted the entire ~/.Skype directory. When I sign back in I can see all my contacts slowly getting reloaded from Internet and after a while all my conversations are reloaded as well.
Using Skype 18.104.22.168 on Linux Mint Debian Edition.
I found that if you go to Options/Privacy/Keep Chat History/Disable History/Apply/Close then log out and log back in, my chat history disappeared. You can then reset it to whatever period you want again - ? 2 weeks.