The majority of available wearable devices require communication with Internet servers for data analysis and storage, and rely on a paired smartphone to enable secure communication. However, wearable devices are mostly equipped with WiFi network interfaces, enabling direct communication with the Internet. Secure communication protocols should then run on these wearables itself, yet it is not clear if they can be efficiently supported. In this paper, we show that wearable devices are ready for direct and secure Internet communication by means of experiments with both controlled and Internet servers. We observe that the overall energy consumption and communication delay can be reduced with direct Internet connection via WiFi from wearables compared to using smartphones as relays via Bluetooth. We also show that the additional HTTPS cost caused by TLS handshake and encryption is closely related to number of parallel connections, and has the same relative impact on wearables and smartphones.