At the start of each player’s Shooting phase, the player whose turn it is can select one CHARACTER unit from their army that is not Battle-shocked and is eligible to shoot. That unit is tasked with extracting a bio-sample from an objective marker, and until the end of that player’s turn is not eligible to shoot or declare a charge.
You're instructed to select a character
unit to perform the action, rather than a character model. That means the entire unit, both the leader and the bodyguards, perform the action. Both suffer the restrictions.