As someone who regularly manages to not only find Ancient Cities so she can decontaminate all the Sculk, but also enjoy her earnings from the City's treasures without getting caught by the Warden? Wool issue. Jokes aside, though, the Ancient Cities have plenty of Wool to provide you with that you can use to nullify Shriekers, Senors, and any other critical compenents that'd potentially set off a Shrieker. What ultimately matters is that you want to use a Silk Touch tool to turn otherwise terrifying forces of nature into "wireless redstone" appliances. To do this: Isolate, Decontaminate, and the rest is history
My guideline for Ancient City: 1. Have enough wool and a decent hoe. 2. Set up a mini base nearby. Have it far enough from the city so that the Warden cannot detect you from there. 3. Always have an easy escape route ready that leads to the base. 4. Don't bother sneaking around the Warden. He literally just smells were you are anyway. Just sprint away through the escape route to your base and wait for two minutes for the Warden to despawn. It takes some time but I never died this way.
