Final answer:
The instrument that would NOT be placed on the Mayo stand for an Exploratory Laparotomy is the suction catheter.
Step-by-step explanation:
When setting up the Mayo stand for an Exploratory Laparotomy, the instrument that would NOT be placed there is the suction catheter. The Mayo stand is a sterile table used during surgical procedures to hold instruments and supplies. The other instruments listed - scalpel handle with blade, Adson forceps, and Gelpi retractor - are commonly used during an Exploratory Laparotomy.