A device including a lower assembly (30) and a cable (32) for deploying the lower assembly (30) in the well (12). The lower assembly (30) includes a pyrotechnic system (72), and a firing assembly further including a module (86) for controlling a power battery (88) and a power module (150). The control module (86) includes arming means (112; 158) of the power module (150) capable of connecting the power battery (88) to the power module (150) upon receiving an electrical arming signal transmitted through the cable (32). It includes means (114; 160) for triggering the pyrotechnic system (72) capable of connecting the power module (150) to the pyrotechnic system (72), upon receiving a distinct electrical triggering signal posterior to the arming signal.