Wriothesley can use the Mono Cryo and Freeze teams to benefit from Cryo resonance. However, as Wriothesley's Charged Attack shatters, Freeze is not extremely consistent. Mono Cryo removes the Freeze aspect in order to slot another Cryo support.
Regarding Weapon Choices:
Flowing Purity: This weapon is more potent if you can reliably clear the Bond of Life. If you can, this weapon is equal or better than .
Regarding Artifact Choices:
Sets
Blizzard Strayer (4):Wriothesley shatters Freeze which makes this set lose valuable uptime. Unlike (4), it cannot be used in Melt teams, and loses versatility.