Ok, here are my 2 cents:
As far as I know, Docker Compose is designed to orchestrate services on a single Docker host or instance. This basically allows you to replicate the full app environment and makes it easy to test the app locally or in a CI environment.
On the other hand, Docker Swarm is designed for running containers at scale. If you have just one node, you don't really need the cluster engine to manage it. So it all depends on your boss 🤔 Is he planning to scale the application to multiple instances in the near future or is he just playing around with Swarm? You're probably overkilling the whole thing if you plan to maintain just a single instance.
Disclaimer: I'm not a dev, but a big DevOps enthusiast who finds these things super interesting, maybe someone else will correct me :)