Is there a way to disable beard growth?

Yes. Take your household into cas.fulleditmode and then untick the box from hair grow (or however it's worded). I had to do that. It's gets to the point I was having to juggle too much. In fact, after the first few times of having my female Sims shave their legs, I turned it off, too. And gave them the clean-shaven legs, instead. For some reason, my young Rock Star doesn't get the notice to shave. I think I managed to accidentally set his beard grow to scruff, or something. I'll have to fix that.