We don't fully know what Cognitive Shadows are, but Mistborn: SH gives a lot of info. Basically, since we exist on 3 Realms, when we die, our Physical returns to the ground, our Spriitual...unknown (but we know that the spiritweb exists and that it takes time to 'decompose")?, and our Cognitive, aka our consciousness, enters the Cognitive Realm. Normally, that consciousness, or self, then moves Beyond the three Realms, to whatever afterlife may be waiting.
However, with enough investiture, either a fresh infusion, or from past actions, your mind can persist for an amount of time (depending on the amount of investiture).
And there are also ways of regaining your body. Or a body.
Returned are Cognitive Shadows stapled back into their bodies with a giant Divine Breath.
Fused are Cognitive Shadows stapled back into a Singer body with Odium's investiture.
Heralds are Cognitive Shadows stapled back into...a body? their body? a body created for them?...with Honor's investiture.
Does that help at all?
At any rate, given that the Heralds are suffused with Honor's investiture, and the ones we see don't have any signs of red (signalling that some of their investiture has been co-opted or corrupted), I don't think Odium would have been able to steal part of their minds to create Unmade.