Indeed, you can't.

In modern Czech, "šaty" is used for women's dress.

In not too distant past, however, "šaty" was also used to generally refer to "clothes", so when talking to grandmas/grandpas or reading old books, you might come across this meaning too. I believe both are accepted in this course. If you want to refer to clothes nowadays you'd better say "oblečení". It's what most people would use. For men's suit, we use "oblek"; if he has no suit (more common), then either "oblečení" to speak generally or pick the one type of clothes you want to refer to (košile, tričko, kalhoty, ...).