O-RAN architecture introduces a new level of flexibility in managing Radio Access Networks (RANs), facilitating the development of different applications. One of these applications is spectrum sharing, in which cellular traffic can share the unlicensed band with WLAN technologies, such as Wi-Fi. A key component of this application is a spectrum classification unit that identifies the communication technology used in the medium to support decision making in the RAN. This classification can be performed using Deep Neural Networks (DNNs) that receive I/Q samples and infer which communication technology is generating the traffic. Despite the high accuracy of DNNs in this task, the inference must be performed quickly to allow timely action to avoid interference. One promising approach to enhancing the performance of DNNs is to use early-exit DNNs (EE-DNNs), which are designed to reduce computations by allowing the inference process to terminate at intermediate layers when a certain confidence level is achieved. In this paper, we explore the application of EE-DNNs for spectrum classification by applying early exits to the Convolutional Neural Network (CNN) used by the ChARM (Channel-Aware Reacting Mechanism) framework. Using the ChARM dataset, we show that an EE-DNN can accelerate inference by 10% and even achieve higher accuracy than a conventional CNN by approximately 2%.