Both the Yamata no Orochi Zoan and Kaido's Seiryu Zoan are popular speculative guesses for the DF that Shiryu's blade might eat. However, I don't think it will be either of them.
Burgess, Augur, Pizarro, Devon, Wolf, Shot, and Doc Q all gained new fruits, yet Shiryu ended up with one previously used by Sanji's former opponent. This is why I believe his sword will instead introduce something new.
I'm thinking it could be the Mythical Zoan Tori Tori no Mi, Model: Garuda. We know Judge's epithet is "Garuda," so it's a recognized mythical creature within the OP world. If Shiryu did have that ability, he would then have two powers connected to Sanji: the Clear Clear fruit and a DF linked to Judge's epithet.
There's also a connection between Asura and Garuda. They both belong to the Eight Legions. Garudas are the mortal enemies of Nagas (dragons or serpents), making it thematically fitting for such an ability to clash with Zoro's King of Hell Three Sword Dragon/Serpent moveset. The name "Shiryu" can also mean "death dragon."
It could even fit the subtle Zoro vs. gold theme, as Garudas are often depicted with golden wings. The other golden-themed opponent is Nusjuro, since the planet Venus can be literally translated as "Gold Star" or "Gold Planet" in JP.