[joezydeco]

So is there a way to do this trick without your hand touching the liquid?

[howderek]

Yes

https://www.youtube.com/watch?v=MLeYYMT-3BM

[hnzix]

Yes, I do this all the time. Hold the bottle vertically with the mouth facing downwards. As the water is pouring out, flick your wrist in an upwards elliptical arc, keeping the mouth facing downwards. It only takes me one or two flicks to create the vortex, and no liquid sprays around or touches me.

It's kind of a swirling motion.