Understandably, I'm not well-versed on Japanese corporate law, but since Iwata didn't name a successor, doesn't this mean that the next head of Nintendo would have to be picked by a special election from the stockholders (much like how Iwata recently "won re-election" to maintain his job)? If so, the next head of Nintendo could push for more sweeping changes than you'd think, having been picked by stockholders fed up with years of tradition, but we'll see.
In any case, as I've stated elsewhere Iwata's left Nintendo in an interesting situation for whoever picks up the torch: the company's not as bad off as it was a year ago in some respects thanks to Amiibo sales, but the Wii U is still practically a dead platform and 3DS is starting to slip in that direction as well. Nintendo right now is probably the most irrelevant in the general gaming landscape than it's ever been before, but NX; mobile support; and franchise licensing are coming. As Reggie noted in the E3 Direct, it's a time of transformation for the company. Iwata's death could be the perfect time to wipe the board clean and start fresh with new leadership that can steer the company in a new direction, but as has been noted Nintendo is an extremely traditional; stubborn; and incestual company so I can't say it's likely that they'll choose a radical new leader.
Personally, whoever takes over Nintendo needs to be young and have little to no ties to the old Yamauchi-era guard. Nintendo's a company in desperate need of new ideas, driven by a bold and charismatic person who is more open-minded towards embracing the West and 3rd parties. If that means hiring outside the company, so be it. When Disney was on the verge of bankruptcy in the 1980s after decades of "What Would Walt have done?", the company was saved in the 11th hour by the hiring of Michael Eisner, a ruthless but charismatic businessman from outside the company who didn't give a **** about "What Would Walt have done?" but knew exactly how to leverage Disney's catalog while pushing towards the future. Frankly, Nintendo needs someone like Michael Eisner to right the ship with new ideas and a fresh perspective, even if it means hiring outside the company.