For me, the thing is whether you can perform kote-gaeshi from outside the shoulder of the arm being manipulated (as well as ahead on the spiral being traced), or whether you are having to perform the technique on the inside of that shoulder (whether you are ahead on the spiral or not).
If you are outside that shoulder, almost anything works, with my preference being what I see Stefan doing in the picture on his website (because I like to ENSURE that uke goes topsy-turvy and this hand position allows one to continue the movement past the bottom apex and back up the other side of the circle).
If you are inside the shoulder, nothing works (my opinion) unless you actively address Uke's cross-lateral arm - because that arm can be used from anything to striking, countering, resisting, readjusting one's line of gravity back inside the base of support, etc. What often goes unnoticed is that folks disregard whether they are outside or inside the shoulder of uke. This is possible because Uke is often more primed to "go with" the technique than to note the differences that become relevant in regards to these two positions.
Additionally, in my experience, it's a tough tenkan maneuver to remain on the outside/ahead of the shoulder when returning for the gaeshi part of kote-gaeshi. Most folks do what I would call a "reversing" of uke's body/energy/body parts - which will almost certainly put you inside the shoulder of uke's.
Here's a video of one common version of what a person can do when inside the shoulder of uke - addressing the other arm directly:
Please excuse the funky music and the slow motion - we were testing our new software, etc., when we put that together. The technique in question the sixth technique executed.