Does this “intercom” have a REST API? Most services do these days. It is often easy to use the Bubble API connector to connect to 3rd party services. This is the typical Bubble approach to integrate to 3rd parties, however sometimes you have no option but to use and or create a plugin. Fingers crossed you can just use the API connector
If it ends up you really do need to manually create an HMAC and nothing else will do it I have previously done it in some plugins, so I know it is possible.