If I understand your question correctly, the closest you’ll get is to create a container that only contains a single statically linked binary. Some Go-based application containers are like this. (If you can build a statically-linked Linux binary of your application, then distributing it via Docker has somewhat minimal benefits.)
Remember that the ability to
docker run anything implies unrestricted root access on the host system, the
docker history of an image can be readily inspected, and a sufficiently curious user can create their own Docker image of your image plus, say, Busybox, and see what was in the base layer. It’s pretty tricky to put actually secret things into Docker images.