I mean, the goal is to undermine Talos, and in order to do that, they need to make people stop worshipping him.

If they wipe out humanity, wouldn't it mean there is nobody left to worship Talos, thereby destorying him completely?

According to a Lore guru (whose name escapes me now), if Alduin were to destroy the world as it is, Talos will still be strong enough to stay as a Divine.

It kind of makes me wonder: how exactly does this whole faith works and how long does it take to completely undermine Talos from the moment the last faithful dies (as in from the second literally nobody believes in him anymore)?

The point is not only to wipe out Talos, but humanity as well.
The Aldmeri Dominion views humans as a blight on the world. Their wish is to eradicate all men from Tamriel. Having Talos as one of the divine is unthinkable, for once he was a man. While they can't make a world wide genocide over men while they don't even control whole Tamriel, they can try to pressure men to reject Talos

I really, really doubt they would actually succeed that way. The Thalmor have no way of knowing who worships Talos and who doesn't, and his faithful don't necessarily have to be Men.

Anyway, I don't really have enough knowledge of Talos' stance in the Wheel to really give a non-made up answer to your question, so somebody correct me.

I'd assume he'd collapse immediately, but the real question is if that was all it took to make Mundus unravel. Which Towers are still online again?

I would imagine that getting rid of Talos is just one step in the path to a Man-less existence. Prior to Talos, the universe didn't crash and burn (although the Towers had a lot to do with that, admittedly). My guess is that Talos is just one of many redundant safeguards that ensure Lorkhan's nature won't be forgotten, and the Thalmor would have to get rid of every single one of those safeguards before considering it suitable to destroy the world.

It has been argued before (though I do not know on which source) that since the falling of White-gold, Snowthroat, etc. Talos is the only safeguard that is keeping us from going back to dawn-like state.