In the end it looks like this is forgotten or lost knowledge, so I used the Set Style action for each property.
However, to speed things up I basically made families for each button type so that I needed to make less changes.
I'd still like to know how to do it with a style sheet though...
Suggestion to Devs If style sheets are a problem, maybe in the 'set style' action there should be just an option to paste in a complete chunk of CSS. That way we don't need to have an action for each property. It's pretty monotonous work..