Re: What is the correct hand placement when do kote gaeshi?
If uke ends up in front of nage before the takedown, there are lots of opportunities for a reversal. I'm skeptical of the NY Aikikai version for that reason. I like the other version better precisely because he does demonstrate a variety of hand positions: body positioning and connection are more important to the technique IMO.
In answer to the OP's question, though: do the version being demonstrated until you are experienced enough to ask for and understand an explanation of the differences among them.