The wyvern can shoot a hot fireball from its mouth thou.
I mean like even though if they are cold blood, their mouth is hot enough to be locked by the infrared missile.
According to fandom and novel, they deployed the 2nd and 4th Escort Flotillas of the JMSDF.
It also can be also Ise(which is part of the Izumo class) or Kaga.
But idk if the manga will use a different escort flotilla compared to the novel.