You could configure dockerd (in the VM) to listen on TCP [1][2], then, back in OpenBSD, define & export `DOCKER_HOST` [3] and from then on use the 'docker' client on OpenBSD [4] without even having to ssh into Alpine.
Warning: I have not yet tested this yet, but it's about the same way as it works on macOS.
Also, I would have probably tried to use boot2docker [5] as guest instead of Alpine.
[1] https://docs.docker.com/engine/reference/commandline/dockerd...
[2] https://docs.docker.com/engine/security/https/
[3] https://docs.docker.com/engine/reference/commandline/cli/
[4] https://www.freshports.org/sysutils/docker/ (< you probably have to build it yourself)