Delay states "you take no action" and move your initiative down. Since the second mind is only allowed a standard action and acts on your initiative, not its own, it can't move the initiative down and would require the rest of you to 'take no action'. You're still just one person, even if you have two minds.
Also, you can't delay to act when the NPCs act. You can delay to just before or just after, but not during. I could see the second mind being allowed to ready an action, but he'd have to specify the conditions as usual.
I don't think this is correct.
The schism'd mind is considered separate in all ways, thus it can delay or ready an action. Nowhere in the schism power does it say that the mind MUST act at the same time as you, or
only on your initiative count. It says that its FIRST action is on your turn and on your initiative, it doesn't say you can't delay that first action or any subsequent actions indefinately for all the power cares. If it were the way you say, it would have to "pass" not delay, and passing is actually not an option, you HAVE to either delay, ready or take your action.
Readying is certainly within the purview, you can ready as a standard action, and that's exactly the action type that the schism'd mind gets.
The consequences of either of the above actions would mean that the schism'd mind would now act at a different initiative than your main mind. And that seems to be ok since it specifies that they are separate and distinct right in the power.
So I don't see anything wrong by RAW or even RAI, with delay or ready.
@unbeliever, Synchronicity is a good suggestion and certainly RAW viable, but I'm not sure this is what the OP is looking for. You use your schism'd minds psionic focus to manifest linked power synchronicity with synchronicity. This nets you an additional standard action next turn. But this only works at higher level and only gets you one turn with 3 actions, which lets you nova, but the OP is looking for a way to get a delayed action, and while you can do this with synch, its not a constant- and I believe it would delay your main mind to the initiative count; no matter which action you chose to delay with.
edit: fixed "spell" ref to "power"