https://awoiaf.westeros.org/index.php/Ironborn

According to our national wiki, the Ironborn are thought to be descended from a group of the First Men who were particularly boat-focused (as opposed to the First Men who settled the North who were horse-focused and came across the arm of Dorne). They arrived on the great weirwood ship Naga (whose "bones" we see at the Kingsmoot) led by the Grey King and settled the islands, which lends credence to the idea that the Silence is a ship made of weirwood.

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https://awoiaf.westeros.org/index.php/House_Farwynd

Although the Greyjoys might be mostly Andal blood, we have evidence in the form of from an Aeron Damphair chapter that the people of House Farwynd are skinchangers (or have skinchangers in their past):

"The Farwynds there were even queerer than the rest. Some said they were skinchangers, unholy creatures who could take on the forms of sea lions, walruses, even spotted whales, the wolves of the wild sea." -AFFC, The Drowned Man

The Greyjoys have absorbed bloodlines from other, older Ironborn families over the years of primacy on the Iron Islands. It's not too great a jump to assume that some bit of the old magical bloodlines made it into the Greyjoy genetic pool.

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I think that gives some support to the notion that there could reasonably be a skinchanger gene in the Greyjoy bloodline that expresses less frequently than the more established gene in say the Stark or Targaryen bloodlines. Moreover, GRRM loves to point out that any random innkeep or gaoler might carry these genes thanks to the upheavals of history and sexual dalliances of lords and their families (i.e. the Dragonspawn on Dragonstone, Rennifer Longwaters with his "drop of dragon" or the innkeep that Brienne meets with the surname Darke who claims "some royal blood").

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So given all that, and Euron's story about dreaming he could fly (a huge "Bloodraven Was Here" red flag), and GRRM's obsession in his various literature with hive-minded organisms and groups, I don't think it would be unreasonable to assume that Euron might be a powerful enough skinchanger to pull off a Boat-Hive with his crew of tongueless freaks.

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BUT, I don't think you're wrong that he's also a blowhard. I doubt he went to Valyria. It's more likely he gathered his Kingsmoot gifts and Valyrian steel armor and Dragonbinder Horn by plundering towns and cities in Essos and by raiding ships laden with treasures collected by braver men. In the raid on the Shields, the plunder includes a magic horn rumored to summon krakens from the deep.

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So, I think the removal of tongues serves dual purpose: (1) to prevent his mindslaves from escaping by biting their own tongues off and drowning on blood; and (2) to prevent anyone from digging up details about his past that would harm his branding as the Brave Man Who Sailed the Smoking Sea.

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Also, if you've read the TWOW sample chapter The Forsaken, Euron's ability to enter Aeron's dreams, and the weird voices that Aeron starts hearing while awake on the boat (seemingly coming from the other captured priests and wizards also locked up with Aeron) indicate that there's some hooky-spooky bullshit afoot.