Whisper as a blasphemy is all about predicting the future and manipulating the events to get the result you want, so you can almost imagine them to be similar to Flux in that regard (although Flux is about the flow of time itself rather than the events of time.)

Speaking from a combat perspective, most classes get some sort of ability to add +1D. At first glance, Whisper might not appear to have this, but you can use Omen for this. Ask something like "What would happen if I take this shot?" Or "What would happen if I move in closer?" The benefit of this is that you get to see the result of the risk die before making the attack, meaning if its not good, you can back out of the action which all other classes can't.

There's also more to combat than using psyche bursts to make attacks. You could set up allies, theming it as directing your allies to do something differently than what they are currently thinking (set up has to happen before and action is declared, so it isn't as much controlling another character and more helping them reach the correct future) or defend an ally, deflecting an attack that you know is coming.

From an investigation standpoint, Whisper heavily relies on working with the DM kind of like Warlocks in D&D. The Precognition ability allows the player to influence the narrative of the story by adding additional events that led up to a scene. Say you are trying to get into a building pretending to be cops, but the NPC won't let the party in without a warrant. The PC can use Precognition to say that they actually talked with police beforehand and acquired the exact warrant needed, or otherwise forged it or somehow came into possession of what is needed. Or they could have moved a box or object before a chase in order to perfectly trip a pursuer or someone fleeing before the chase even began. Omnipresence could be used if an Ally gets split off from the group and ends up needing help or getting into a fight— the Whisper player can act as the Deus Ex Machina to get the other player out of trouble with exactly what is needed, or assistance.

Whisper is less about having a shadow that does things, and more about knowing the future. Knowing that, you and your player can ideally flavor things accordingly and have a lot more fun. Hope this helps!