watchtower/docs/stop-signals.md

When watchtower detects that a running container needs to be updated it will stop the container by sending it a SIGTERM signal. If your container should be shutdown with a different signal you can communicate this to watchtower by setting a label named com.centurylinklabs.watchtower.stop-signal with the value of the desired signal.

This label can be coded directly into your image by using the LABEL instruction in your Dockerfile:

LABEL com.centurylinklabs.watchtower.stop-signal="SIGHUP"

Or, it can be specified as part of the docker run command line:

docker run -d --label=com.centurylinklabs.watchtower.stop-signal=SIGHUP someimage