The spread of the Internet of Things (IoT) and cloud services leads to a request for secure communication between devices, known as zero-trust security. The authors have been developing CYber PHysical Overlay Network over Internet Communication (CYPHONIC) to realize secure end-to-end communication among devices. A device requires installing the client program into the devices to realize secure communication over our overlay network. However, some devices refuse additional installation of external programs due to the limitation of system and hardware resources or the effect on system reliability. We proposed new technology, a CYPHONIC adapter, to support these devices. Currently, the CYPHONIC adapter supports only IPv4 virtual addresses and needs to be compatible with general devices that use IPv6. This paper proposes the dual-stack CYPHONIC adapter supporting IPv4/IPv6 virtual addresses for general devices. The prototype implementation shows that the general device can communicate over our overlay network using both IP versions through the proposed CYPHONIC adapter.