I'm disabled and find it difficult to rotate objects with Z, because I can't hold Z and use the mouse at the same time.
Maybe if you hold LMB for free rotation see Sims)
I don't know of any other suggestions but, they do sell mouses with additional buttons on them that you can program/customize so you could click Z (or any other button) on the mouse along with the standard Left/Right Click buttons. Sorry if that's not what you're looking for.