"running shoes" was right in one of the previous lessons. And it is right any way. At least in Canada.
Can anyone who is Ukrainian confirm that they use the word кросівки in normal conversation? I lived in Ukraine for a while and don't remember ever hearing it.
Russians call it "кроссовки" from the word "кросс" - running cross country. It is very normal word. Very possible the Ukrainians do the same. The word is relatively new. It didn't exist 30-40 years ago.