If I'm understanding you correctly, I think you're saying you've already wound 'hanks' into 'cakes' using your tinker toy swift, right?
Or, is your yarn ALREADY balls from which you can pull the center tail to knit, or the outside tail to knit?
If your yarn is ALREADY balls that can be knit from a 'center pull' or from the outside, you DON'T NEED TO wind it further. And if this is so, please DON'T wind it. It puts undue stress on your yarn, or, I should say, unnecessary stress.
Should you work from the center pull tail? I do if I can find the darn thing. If I can't without pulling out a hideous hunk, I just knit from the outside.
I don't think it matters one bit.
With a colorway like NORO, I just make sure that I do the same with ALL BALLS cuz the colorway is distributed in sequence. So I either ALWAYS start from the center pull, or ALWAYS start from the outside.