How to send a signal to a Docker container without affecting restart policy?

TIL that docker kill means kill in the sense of "make it dead", as opposed to the POSIX sense of "send a signal".

We have several containers that we need to send a SIGHUP to in order to reload configuration, but this causes them to ignore their restart policy of "always", which isn't what we want.

What's the best way to send signals to these containers without affecting their ability to auto-restart?

To more clearly demonstrate the issue we're seeing, take the following example.

We have some container that has a restart policy set to always

$ docker inspect cloudwatch-exporter | jq .[].HostConfig.RestartPolicy
{
  "Name": "always",
  "MaximumRetryCount": 0
}

We reload the config at some point using docker kill:

$ docker kill --signal=SIGHUP cloudwatch-exporter
cloudwatch-exporter

Some time later, something happens that kills the process. To simulate this, I'll send a signal within the container:

$ docker exec cloudwatch-exporter bash -c "kill 1"

At this point, the container is dead and won't restart:

$ docker ps -a | grep cloudwatch-exporter
c7827204bba5        prom/cloudwatch-exporter:cloudwatch_exporter-0.8.0                                "java -jar /cloudwat…"   20 hours ago        Exited (143) 3 minutes ago                            cloudwatch-exporter

What alternatives do we have for using docker kill? For many cases docker exec works, but it won't work for any container that only contains a single static-linked binary.