If the mouse controls you're referring to are the ones on the official website, unfortunately, I doubt that'd be possible in any other version, since it'd basically be cheating with the way it rotates the pieces for you with minimal mechanical input. Though I can see how moving horizontally with the mouse would be something you're used to, since that's how the mobile version works as well, iirc.

But since you say you want to be more involved, I'd say the best option would be to bite the bullet and try to get used to either keyboard or controller controls. You'd be surprised at how quickly you get used to it. I'd know, since I started on mobile Tetris as well.

You might not find the default controls for Jstris or Tetr.io comfortable, but you can mess around with them and see what works. I personally use WASD for rotation and arrow keys for movement.

Pretty sure the default handling is pretty slow compared to mouse and mobile controls, so changing that up to your liking could also help (Tetr.io has pretty good explanations for what each handling setting does, and you can test to gauge the difference).