I have actually been waiting for this battle for ages now :O i have a whole speech and dissertation ready. I'm just glad it's Cosmos and not Eternal Sailor Moon cause that would be a stomp.
I actually say that Cosmos should be able to resist the void manipualtion of hades. For several reasons:
Hades sword is described as,
" Those cut by the Sword of Hades are annihilated completely in body and soul, being removed from the Wheel of Samsara and sent to the World of Emptiness where time does not exist, being unable to ever revive or reincarnate"
1. Scaling from Sailor Saturn, we know very well that Senshi can exist without body and soul and can come back from both being destroyed. You would need to destroy the starseed, the concept of her existence, but the Lambda power can regenerate indefinately.
2. The removing from the Wheel of Samsara negates reincarnation, a concept that exists in Sailor Moon verse. (Princess Serenity reincarnated into Usagi Tsukino etc.) Preventing Cosmos from being able to reincarnate is something she can't stop, but reincarnation was never battle oriented (it takes an indefinite time). Removing this ability won't hinder Sailor Cosmos as her regneration power is seperate.
3. Sent othe world of emptiness where time doesn't exist, isn't a threat at all to Cosmos. It's an elaborate BFR that Cosmos has already shown work around as Sailor Moon in as early as the second arc.
a. The Corridor of the spacetime door is a space-less and time less void where things get erased
b. Senshi with Pluto's power (Cosmos by virtue of being cosmos has pluto's power) have been able to to enter and leave this time-less, existence erasing void without issue as well as travel through it without being affected .
ab. I argue that Cosmos should be able to leave the World of Darkness using Pluto's power as well as her own multi universal range, teleportaiton etc. and be able to resist it's existing erasing effects (which leads me to point 4)
bb. Also, the galaxy cauldron auto erases everything it touches and they were able to exist without effort inside of it, so that's added resistencee to existing in a place that erases things by nature
4. Even from the Second arc, Sailor Moon showed resistance to existence erasure (the dark crystal erases things near it and was erasing the people and earth just by it's prescense alone). She also shown (via Neo Queen Serenity) that she can bring those things that were erased from existence by the dark crystal back. This is just base alone.
Now fast forward, even though she already was shown power to bring things back from non-existence, at her strongest from as Eternal Sailor Moon, she coudln't undo the erasing effects of the Galaxy Cauldron and admitted defeat and despair at this reality. However, then comes the Lambda power whose regenerative power is so beyond, that it could bring back the sailor cystals that were erased by the Galaxy Cauldron.
So to recap
erased from existence < base sailor moon's power <eternal sailor Moon's power < galaxy cauldron's erasure powers < Lambda Power
Now, let's bring out Sailor Chaos. Sailor Chaos completely laughs in the face of the lambda power. She destroys something and it's done. That's it. Nothing can bring it back in verse. it's the very reason why Sailor Cosmos ran away from her fight because to her, it meant nothing anymore if she couldn't bring back all her loved ones who were destroyed. And made her finally decide that she's gonna have to reset the world and start all over again from the beginning.
Now, while Sailor Chaos's void manpualtion >>>>>>>>>>> Lambda power. Sailor Cosmos has reistence to it (only for herself) as she faced Sailor Chaos and lived to tell the day.
So in conclusion:
TL;DR Sailor Cosmos should be able to survive having her body and soul destroyed and can regenerate from it. As well she will be unaffected by being sent to the World of Emptiness as via much scaling she's shown resistance from being able to exist in existence erasing timeless void and should be able to leave said world.
And this is just one argument for just dealing with Hades sword. My god. Not even the other things Hades have. But I'll wait to see how the tide responds to this before even going further.