WARNING: The following contains spoilers for Demon Slayer: Kimetsu no Yaiba Season 2, now streaming on Funimation, Crunchyroll and Hulu.
Despite his incredible strength and heroic efforts, Demon Slayer's Tengen Uzui needed a lot of help to defeat Gyutaro. Upper-Rank Six proved to be no pushover in the "Entertainment District" arc, nearly claiming the life of a Hashira from beyond the grave. Gyutaro's deadly poison was mere moments from killing Tengen before Nezuko's Blood Demon Art saved the Sound Hashira's life. Had Nezuko not been there, Tengen would've been the 16th Hashira to lose his life battling Gyutaro -- and the 23rd to go into Yoshiwara and not return.
Although Tengen considers himself one of the weakest Hashira -- perhaps rightfully -- there's little reason to believe most of the others would have fared any better against Gyutaro. After all, Tengen is a former shinobi with resistance to poison and he still struggled to fight off the poison's effects well enough to keep fighting effectively. Assuming none of the other Hashira are former shinobi who can resist poison and stop their own hearts to halt its spread, that only leaves one who could have defeated Gyutaro and survived his poison without Nezuko's help: Shinobu Kocho.
Gyomei Himejima was the first person in Tengen's mind when thinking of incredible warriors, and Muichiro Tokito is so talented that he became a Hashira in a scant two months. Even Iguro Obanai, the Serpent Hashira whom Tengen had called for backup, referred to Gyutaro as the "lowly" Upper-Six.
So, it stands to reason that these Hashira who may be worlds above Tengen in strength could have defeated Gyutaro. However, it feels far less likely that they, or anyone, could defeat him without receiving a single scratch -- and that's all it takes for his deadly poison to take hold.
Shinobu Kocho, on the other hand, is an expert in all things poison and was shown in Demon Slayer's "Natagumo Mountain" arc to always carry various antidotes with her. Even if someone like Gyomei or Muichiro could've defeated Gyutaro, they'd have been helpless to fight his poison. Gyutaro never would have become an Upper-Rank if he could possibly be defeated without wounding his opponent even once. Considering even Tengen's resistance to poison wasn't going to save him from Gyutaro's, any other Hashira besides Shinobu who even got nicked by Gyutaro would be facing certain death.
Tengen owes his life to Nezuko's get-out-of-jail-free Blood Demon Art, while Shinobu is the only Hashira who wouldn't need to bring Nezuko along in the first place. Although Shinobu is too physically weak to decapitate demons, she's blindingly fast and uses her special sword to inject demons with Wisteria poison.
Wisteria poison is anathema for demons, a substance that is actually capable of killing them with a large dose. Gyutaro showed a surprisingly low tolerance for it, being rendered helpless by a small amount on the tip of a Kunai. If Shinobu and Gyutaro fought and poisoned one another, the former would most likely be able to cure herself, whereas a high enough dose of Wisteria would be enough to kill even an Upper-Rank.
Shinobu Kocho, the Insect Hashira, makes up for her lack of strength with incredible speed and a plethora of poison, so she'd probably have had a somewhat easier time battling Gyutaro and Daki than Tengen did. All she would have to do is stab each of them once and wait for them to die from Wisteria poison. Not that this would be simple -- they are Upper-Ranks after all. While it seems that many of the Hashira may have defeated Gyutaro more easily than Tengen and the boys did, poison is Shinobu's specialty. Nezuko's Blood Demon Art is tremendously valuable, but Shinobu's the one Hashira in Demon Slayer who wouldn't have needed it.