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If I have a Seeker of Skybreak and Mesmeric Orb on the battlefield, and exactly one Emrakul, the Aeons Torn in my library, and I play Shelldock Isle as my land for turn, I can, in response to the Hideaway trigger, mill myself infinitely until I get down to 4 cards in the library without hitting an Emrakul and getting a shuffle trigger. I can even handpick the other three cards involved by continuously milling until I see the other 56 cards of my deck outside of my library (and don't hit Emrakul).

So is it legal to explain the process to my opponent, show him my deck so he can be sure that I actually have the necessary cards, and then shortcut to that gamestate, assuming no interaction from either player?

That infinite combo doesn't allow you to describe the gamestate at the end of X iterations, so no you cannot do that.

If you do what you're trying, you'll likely be the receiver of a "slow play" violation. 

3.3. Tournament Error — Slow Play

Penalty - Warning

Definition
A player takes longer than is reasonably required to complete game actions. If a judge believes a player is intentionally playing slowly to take advantage of a time limit, the infraction is Cheating — Stalling.
It is also slow play if a player continues to execute a loop without being able to provide an exact number of iterations and the expected resulting game state.

Examples
A. A player repeatedly reviews his opponent’s graveyard without any significant change in game state.
B. A player spends time writing down the contents of an opponent’s deck while resolving Thought Hemorrhage.
C. After 3 minutes into a round at a Pro Tour Qualifier, a player has not completed his shuffling.
D. A player gets up from his seat to look at standings or goes to the bathroom without permission of an official.

Philosophy
All players have the responsibility to play quickly enough so that their opponents are not at a significant disadvantage because of the time limit. A player may be playing slowly without realizing it. A comment of “I need you to play faster” is often appropriate and all that is needed. Further slow play should be penalized.

Additional Remedy
An extra turn is awarded for each player, to be applied if the match exceeds the time limit. If multiple players on each side are playing the same game (such as in Two-Headed Giant) only one extra turn is awarded per team. This turn extension occurs before any end-of-match procedure can begin and after any time extensions that may have been issued.
No extra turns are awarded if the match is already in extra turns, though the Warning still applies.
If Slow Play has significantly affected the result of the match, the Head Judge may upgrade the penalty.

Goth is right. There is a deck called the 4 horseman that does something similiar to this (I.E Mesmeric Orb to mill 3-4 Narcomoeba + Dread Return + some sort of win-con like Shaarum the Hegemon whilst shuffling Giant Floating Jellyfish of Doom to "recycle" their GY to prevent total self milling.

I think that slow play rule may be new, but either way it is a rule now saying NO to you and the deck I mentioned.