Buy a cheap ESP8266 development board and apply for an MQTT service with a certain free quota from EMQX (or other cloud service providers). You can then use this small development board to send broadcasts within the local network (including WOL requests), paying only a few dollars for the development board. Running such a simple Arduino program consumes much fewer resources compared to running Node.js within the local network, and it's also more power-efficient.
It should work. This article describes setting up port forwarding on a publicly accessible router, then using a cloud function to send a wake-up packet to that port. The router's port forwarding then broadcasts the packet.