Tell sensors and shriekers apart
The sensor receives vibrations, the screamer raises the alarm. Naturally created screamers are capable of summoning Warden; a screamer transported by the player does not do this normally. You cannot consider every block found or placed to be the same threat. Reference: Minecraft: Rock Screamer.
Before entering, leave excess equipment in a chest outside the city, write down the X/Y/Z of the exit and grab wool, shears, food and night vision if available. The dark effect of the alarm is not the same as the absence of torches.
Plan for one specific chest
Lay a wool path from the verified entrance. Before opening, inspect the sensors nearby and behind obstacles. The wool between the vibration source and the sensor blocks this path, but one carpet underfoot does not isolate the sound of a chest being opened.
When accessing, cover the screamer with fur on all sides without stepping on it. Crouching helps avoid footstep vibrations, but does not cancel out all events like opening a container. Don't break adjacent blocks blindly: check what the action will hear first.
A backup attempt after death requires a separate procedure: Recovering your items after death without dying again.
If the Warden appears
Abandon the chest and take the wool route. Don't shoot the boss to check damage and don't build a pillar as a guarantee of cover: his sound attack goes through blocks.
Warden hears and sniffs out the player; wool solves only part of this problem. Keep your distance and do not create new events nearby. A shield and a thick regular wall don't make this a safe fight.
Disarming traps of other structures is discussed here: Exploring structures: traps, chests and a way back.
