Euron, certainly - whether its Balon or Theon, that dragon egg is being used on someone.
With that said, if Balon and Euron had died while Eddard Stark, Jon Arryn and Robert Baratheon were still in the picture, and Westeros hadn't yet erupted into civil war, I think Theon is in a much better position than people realise.
If a healthy Theon returns to Pyke with support from the Iron Throne as legal heir, Asha's support is going to melt away pretty quickly. Remember, Asha's Kingsmoot backers may be progressive among the Ironborn, but they would be fairly typical lords on the mainland. Rodrik's motives would be more nuanced and personal, but guys like Lord Baelor Blacktyde, Ser Harras Harlaw, Lord Meldred Merlyn, and Lord Sawane Botley are going to throw their weight behind Theon for the simple fact that they most likely follow male primogeniture, as most Westerosi do. Asha's claim doesn't even really come into it in this scenario, only in so far as she is her brothers heir until he has children of his own. In this scenario, I think Asha would probably offer something similiar to that which she offered to Victarion in AFFC (whether Theon is smart enough to take her up on it is another question, although odds are better than with Victarion).
There is this notion that the Ironborn have never been ruled by a cultural outsider, when in fact the opposite is true: historically there have been a plethora of reformers and mainland-fostered Ironborn Kings/Lords, while they literally have never had a ruling Queen (and if Asha does rule at the end, I suspect it will take some extremely extentuating circumsances to ultimately come to pass). A recent example is Lord Baelor Blacktyde, who returned to the Iron Islands after eight years essentially as a full-blown Reachman, and yet his inheriting of his seat wasn't disputed in the slightest. It took Harmund Hoare aggressively forcing the Faith as the new dominant religion for the Shrike to lead a Rebellion - the only real Shrike like figure currently is Aeron, and if he wasn't willing to kill Euron, I doubt he'd become a kinslayer for his nephews crime of supposedly becoming a soft greenlander. The only real wildcard is if Aeron calls a Kingsmoot to crown Vic, but even Damphair knows the only chance for Ironborn independence is when Westeros is vulnerable.
Following Theon is also in the best interest of the more reasonable Ironborn lords - from their perspective anyway; all of these guys want an end to the Old Way and to form closer trade and political ties to the rest of Westeros and, wouldn't you know it, the new (officially sanctioned by King Robert) Lord Reaper of Pyke is close friends with the young heirs to Winterfell, Seaguard, Riverrun, etc. and as far as the Harlaws and Botleys know he's going to rule the Iron Islands as any mainlander would. Lastly, no one wants a repeat of the Greyjoy Rebellion, if Theon (from the mainland perspective) is usurped by his sister or one of his uncles, it will be their castles and towns getting raised.
So, at mimimum, Theon has the backing of the "Progressive" Ironborn, but I think he has Victarion's support too:
"Lord Captain of the Iron Fleet, and a fearsome warrior. I have heard them sing of him in the alehouses."
"During my lord father's rebellion, he sailed into Lannisport with my uncle Euron and burned the Lannister fleet where it lay at anchor," Theon recalled. "The plan was Euron's, though. Victarion is like some great grey bullock, strong and tireless and dutiful, but not like to win any races. No doubt, he'll serve me as loyally as he has served my lord father. He has neither the wits nor the ambition to plot betrayal."
Theon II, A Clash of Kings
And the following quote seems to support Theon’s line of thinking:
"Obedience came naturally to Victarion Greyjoy; he had been born to it. Growing to manhood in the shadow of his brothers, he had followed Balon dutifully in everything he did. Later, when Balon's sons were born, he had grown to accept that one day he would kneel to them as well, when one of them took his father's place upon the Seastone Chair. But the Drowned God had summoned Balon and his sons down to his watery halls, and Victarion could not call Euron "king" without tasting bile in his throat."
The Reaver, A Feast for Crows
Theon is wrong about a lot of things, but his assesment of his uncle here is one of the few times he's on the money. If dutiful Victarion backs his nephew, that's going to galvanise a lot of the captains who normally wouldn't look twice at someone who dresses as dandily as Theon. Likewise, when respected reaver, Dagmer Cleftjaw, backs up and vouches for Theon, that's going to mean a lot to the reaving class. Asha could definitely use her tactic of humiliating Theon through casual displays of Ironborn masculinity as she did in Clash - the problem with this is that it isn't going to put Asha on the Seastone Chair and at bare minimum; is likely going to get her brother killed (she's smarter and a better person than that).
So while I don't think Theon would be popular, or even a particularly competent Lord Reaper of Pyke, I think the popular opinion in the fandom that Theon has zero support on the Iron Islands comes from those who possibly did not pay close attention to the Ironborn politics showcased in the book (having biased POV's in Damphair and Vic doesn't help either, when in reality both of those two are cultural extremists in ways most Ironborn aren't). The fact that Theon is a huge doofus ia certainly a contributing factor as well.
If Theon can hang on for a year or so of peace without fucking everything up, then I think he's in a good position to improve his public image among the predominate reaving class - with a successful campaign against the Westerlands, alongside the Starks and Tullys. While he's by no means Stannis Baratheon or Robb Stark, Theon's military education from Rodrik Cassel and Eddard Stark has taught him that the Ironborn will need an actual strategy to make any headway when it comes to war with the mainland (which makes him somewhat of a rarity on the Isles). If he could sack Lannisport and defeat the Farman fleet, his stock would have risen considerably, and he could have proven to be the crown-loyal Lord Reaper of Pyke that Ned and Robert hoped to raise up.
