Emotions expressed by humans can be identified from facial expressions, speech signals, or physiological signals. Among them, the use of physiological signals for emotion classification is a notable emerging area of research. In emotion recognition, a person’s electrocardiogram (ECG) and galvanic skin response (GSR) signals cannot be manipulated, unlike facial and voice signals. Moreover, wearables such as smartwatches and wristbands enable the detection of emotions in people’s naturalistic environment. During the COVID-19 pandemic, it was necessary to detect people’s emotions in order to ensure that appropriate actions were taken according to the prevailing situation and achieve societal balance. Experimentally, the duration of the emotion stimulus period and the social and non-social contexts of participants influence the emotion classification process. Hence, classification of emotions when participants are exposed to the elicitation process for a longer duration and taking into consideration the social context needs to be explored. This work explores the classification of emotions using five pretrained convolutional neural network (CNN) models: MobileNet, NASNetMobile, DenseNet 201, InceptionResnetV2, and EfficientNetB7. The continuous wavelet transform (CWT) coefficients were detected from ECG and GSR recordings from the AMIGOS database with suitable filtering. Scalograms of the sum of frequency coefficients versus time were obtained and converted into images. Emotions were classified using the pre-trained CNN models. The valence and arousal emotion classification accuracy obtained using ECG and GSR data were, respectively, 91.27% and 91.45% using the InceptionResnetV2 CNN classifier and 99.19% and 98.39% using the MobileNet CNN classifier. Other studies have not explored the use of scalograms to represent ECG and GSR CWT features for emotion classification using deep learning models. Additionally, this study provides a novel classification of emotions built on individual and group settings using ECG data. When the participants watched long-duration emotion elicitation videos individually and in groups, the accuracy was around 99.8%. MobileNet had the highest accuracy and shortest execution time. These subject-independent classification methods enable emotion classification independent of varying human behavior.