If you feel more comfortable putting him in a tub, then go for it. If you can get the lights he needs on the tub then it'll be the same as dividing the tank.

If he keeps the shaking up after you get them separated, I'd definitely take him to a vet. It could be stress but it could be something more serious if it keeps up. He might have neurological problems if it isn't stress. It doesn't sound like too big of an issue and he could live a normal life. A vet could tell you more though.