Nano-drones, distinguished by their agility, minimal weight, and cost-effectiveness, are particularly well-suited for exploration in confined, cluttered and narrow spaces. Recognizing transparent, highly reflective or absorbing materials, such as glass and metallic surfaces is challenging, as classical sensors, such as cameras or laser rangers, often do not detect them. Inspired by bats, which can fly at high speeds in complete darkness with the help of ultrasound, this paper introduces \textit{BatDeck}, a pioneering sensor-deck employing a lightweight and low-power ultrasonic sensor for nano-drone autonomous navigation. This paper first provides insights about sensor characteristics, highlighting the influence of motor noise on the ultrasound readings, then it introduces the results of extensive experimental tests for obstacle avoidance (OA) in a diverse environment. Results show that \textit{BatDeck} allows exploration for a flight time of 8 minutes while covering 136m on average before crash in a challenging environment with transparent and reflective obstacles, proving the effectiveness of ultrasonic sensors for OA on nano-drones.