Activity recognition using accelerometer sensors has been extensively studied due to their low cost and low power consumption. However, numerous challenges remain in achieving robust, highly generalizable activity recognition across a broader range of activities. To address these challenges, the use of wearable cameras, which can capture more detailed visual features, has drawn increasing attention. On the other hand, camera images may include human faces and other privacy-sensitive information, leading to concerns regarding user acceptance. In this study, we investigate the trade-offs between recognition performance and user privacy in activity recognition using small wearable cameras. Specifically, we explore how different combinations of accelerometer data and privacy-processed hand images impact recognition accuracy while preserving privacy. As a case study, we focused on six types of desk activities (typing, mousing, swiping, drinking, writing, and others). We compared the recognition accuracy of accelerometer data alone, raw images, privacy-processed images, as well as combinations of accelerometer data with raw images and privacy-processed images, all captured using a wrist-worn wearable camera. The results highlight the effectiveness of our approach in balancing activity recognition accuracy and privacy preservation, offering insights into the trade-offs involved in privacy-aware wearable sensing.