Well I don't know if Shrines are even confirmed but I've got some questions that cannot be answered just yet:
Will The Sheogorath Daedric Shrine exist?
Will there be a different Sheogorath? (Well... Since y'know... I don't want to bring out spoilers)
Maybe Haskill will be answering the shrine?
Are the shrines even in?
Will there be a shrine to Mehrunes? (EDIT: Probably not, he is DEAD banished into Oblivion)
(Edit Questions): Will there be a shrine for Jyggalag?
Is The True Sheogorath Really Gone?
But most importantly: Will There Be Cheese For Everyone!?!?!?!?!?!?

In The Loving Memory Of Sheogorath: ???-3E 433 (I think it was the Oblivion year?) or 4E 0

I should stop you there on Dagon. He was not killed, he was cast back into Oblivion.

EDIT: This is the journal entry you get, "Martin shattered the Amulet of Kings and transformed himself into an avatar of Akatosh, the Dragon God of Time. In dragon form he banished Mehrunes Dagon to Oblivion and ended the Oblivion Crisis, and then vanished. Whether he is dead, or has ascended to join his ancestor Tiber Septim, no one knows." http://www.imperial-library.info/content/light-dragonfires

But about Sheogorath, His shrine will probably still be there IMO because there is no one that told people outside SI what happened in the Isles. Just like at the end of Tribunal, *SPOILER* when Azura tells you that it will take some time for people to realize that Almalexia and the Tribunal has ended, even if you tell them they shove you off.

I imagine there will be shrines. They were in in the three previous games. I'd doubt they'd take them out.

Sheogorath will be the same god as before. Even if the champion of Cyrodiil became Sheogorath, or otherwise.

Mehrunes isn't dead. He was just banished back into Oblivion.

Maybe Skyrim will read off any old saved games you got to see who your old character was, and copy the appearance and render them in game with a Shivering Isles style outfit.

It would be kind of ridiculous for the followers of Sheogorath to destroy his old statues just to rebuild new ones when they wouldn't know the difference. Think about, even the people of the isles didn't notice a change.

I'm of the belief that your character (whether that is the CoC or someone else) "assumed the mantle" completely eventually, and took on the form and personality of Sheogorath. Making him/her a full on daedric prince. Obviously they couldn't do that at the end of Shivering Isles because; In being a daedric prince you would not be able to re-enter Mundus. Meaning, no going back to Cyrodiil for you. That would have pissed a lot of people off. Plus, Bethesda is quite the fan of leaving things open to our own individual interpretations so we can have all kinds of debates

I'm personally far more interested in Jyggalag's fate. Will/Can he create a new realm of Oblivion for himself? Will he have gained followers; And if so will we get a quest involving him?

Sheogorath is still Sheogorath to anyone except maybe Sheogorath.

I just finished SI again myself and was wondering the same thing.