You have Xiangling, right? Then you can use her for Pyro-based attacks, especially her burst, which can deal big damage, and it still active when you swap your characters. So you can just pop her burst, and then change to your main character.
There’s also Amber, which can still be useful for dealing Pyro damage using her burst, since it only costs 40 Energy, or you can use her charge attacks, which also imbues Pyro element.
But if you don’t want to use Pyro characters, then you need to act quick, and kill the Cryo Fatui ASAP, before he could use his Cryo Shield.