Just for posterity's sake, this is the relevant rule that governs this scenario:
400.5. The order of objects in a library, in a graveyard, or on the stack can't be changed except when effects or rules allow it. The same is true for objects arranged in face-down piles in other zones. Other objects in other zones can be arranged however their owners wish, although who controls those objects, whether they're tapped or flipped, and what other objects are attached to them must remain clear to all players.
So if the zone in question is not the library, graveyard, or stack (which it isn't, we're talking about the hand, although there is also the battlefield and exile) then the order of objects in that zone can be arranged any which way but Sunday.
Also, while technically the graveyard is an ordered zone, you're allowed to fiddle with the order of the graveyard:
3.14 Graveyard Order
In formats involving only cards from Urza’s Saga™ and later, players may change the order of their graveyard at any time. A player may not change the order of an opponent’s graveyard.
Only a select few cards actually care about the order of the graveyard, and it was decided early on (apparently, around the time of Urza's Saga) that maintaining the order of the graveyard just wasn't important enough to justify a game loss for failure to maintain board state. So in reality, the library and the stack are the only zones whose order actually matters, and let's face it - most people don't even realize the stack is a zone. I mean, we construct the stack in our head from memory of what was played and triggered when. We don't put the cards out on the table or anything.
So the good rule of thumb is, for the casual player, if it's not a library, you can probably shuffle it any time you want. Just don't be a jerk.