I've removed many dozens of headset cups (mostly of the classic loose ball type) with various non specific tools. A hammer and a long slot blade screw driver of drift punch. Steel headset cups have little issue with this method. Al cups do need a slightly softer hand and therefore more time/repositioning of the driver. But in general it only takes a minute or three to knock out a cup with a handful to a half dozen driver whacks around the skirt.

The cool trick is to do the top cup and be able to catch it as it pops up in the air before it hits the floor. Andy