The Sicilian dragon seems the most appropriate - sharp, counter-attacking, highly theoretical, with a fianchettoed bishop on g7 raking the queenside. Rather you than me, though!
Grunfeld-like openings against e4
I would say the Alekhine for the exact reason that I hate the Alekhine and Grunfeld.
Both openings involve White getting the big, mobile center where Black's idea is that White is over-extended and attacks the White center with pieces.
When you talk about the 5 types of center - Blocked, Mobile, Static, Open, and Dynamic, the Grunfeld and Alekhine are literally the main sources of the Mobile Center.
The type of center is exactly the reason for my combination of choices as Black, the French and the King's Indian Defense, the two main defenses that most often result in the Blocked Center.
So the Alekhine is pretty much your answer if you are a Grunfeld fanatic, literally the two openings I hate most in the game of chess!
What would you recommend as white?
There is no White equivalent unless you want to do something whacko like the Elshad System (1.c3/2.Qh4) where Black gets a mobile center.
It's just like how I have no equivalent to the French and King's Indian. Playing White is a different beast!
The Grunfeld defense can be summarized as
1 fianchetto the king bishop
2 OO
3 throw the c and d pawns into the center of the board
The only defense against 1.e4 that is similar is the Sicilian Accelerated Dragon. Bent Larsen often played the SAD and the Grunfeld.
FYI, the Catalan is a Grunfeld attack.
See the old book Zoom001 by Larsen and Zeuthen.
I've been having a lot of success with the Grunfeld defense and I am looking for an opening similar to that against e4.