Asthma is a chronic respiratory condition that affects millions of people worldwide. While this condition can be managed by administering controller medications through handheld inhalers, clinical studies have shown low adherence to the correct inhaler usage technique. Consequently, many patients may not receive the full benefit of their medication. Automated classification of inhaler sounds has recently been studied to assess medication adherence. However, the existing classification models were typically trained using data from specific inhaler types, and their ability to generalize to sounds from different inhalers remains unexplored. In this study, we adapted the wav2vec 2.0 self-supervised learning model for inhaler sound classification by pre-training and fine-tuning this model on inhaler sounds. The proposed model shows a balanced accuracy of 98% on a dataset collected using a dry powder inhaler and smartwatch device. The results also demonstrate that re-finetuning this model on minimal data from a target inhaler is a promising approach to adapting a generic inhaler sound classification model to a different inhaler device and audio capture hardware. This is the first study in the field to demonstrate the potential of smartwatches as assistive technologies for the personalized monitoring of inhaler adherence using machine learning models.