There should have been a disclaimer, and here it is: in this type of guide, I cover a couple of classic weapons suitable for the character (excluding the signature weapon with some exceptions). This is not a detailed guide but a surface analysis aimed at quickly helping you set up a pre-built setup. Also, everything was sneakily taken from the beta, so some things may work/not work in the release. Forewarned is forearmed.

What catalyst to use for Wriothesley 

Tulaytullah's Remembrance

An excellent choice. High base damage will serve well in Mono Cryo teams, despite the characteristic catastrophic attack drop. Critical damage as the top stat and a ton of affixes in the passive. It doesn't buff the ultimate, but nobody's perfect.

The Widsith

Who would have thought that the "casino" with extravagant passive stats and a cooldown for an eternity would end up here? But think about it: evaluate the statistics of wins, not their size. In a Mono Cryo team, it's definitely not worth taking, and getting rid of the roll's pursuit of elemental mastery is difficult.

Memory of Dust

With a shield, of course. Stacks accumulate quickly, so maintaining their maximum level is not a problem.

Skyward Atlas

Worse than all of the above (even "Dust" without a shield), but if you have three of them from the standard - or, my condolences, event - pull, you can use it without worry. "Atlas" is more stable than "Widsith," so you don't need to memorize switch timings and hope for a favorable note.

For more detailed information, refer to the guide!