Restart Docker Container Without root privileges

Hello, I have a mumble server running as a docker container.

I'm using lego to generate let's encrypt certificates using dns challenge as an unprivileged user.

My problem is that I need to restart the mumble server so that it can reload the ssl certificate, which means restarting the docker container.

Is there any way to do this withuot adding the user to docker group, since there are security issues with that group where it's easy to escalate to a root user.

I thought about maybe a user level systemd service could be able to do it, but wan't to hear your opinions?

EDIT: I mention mumble specifically here, but this can apply to any server that requires manual reload of ssl keys, like postfix for example. I'm also not againd the idea of converting to something like kubernetes or even podman ( which would be harder cause of file permissions on all my binds ) if they can allow for woking on the container without root privileges.