Is the best way to update a running Service by using another service? [C#]

I need to find a reliable way to update a running Windows Service (Service.exe).
The service is run under the LocalSystem account whereas the logged-in user is in a non-admin User account.

My current solution would be as follows:
- The Service.exe checks for updates (files) regularily
- When an update it found it starts another service (Launcher.exe) that would stop the Service.exe, copy over the files, restart Service.exe, then stop itself

After doing some online-reading and from some of my previous forum posts I beleive this would be the appropriate solution - but before I go ahead I wanted to check with all the guru's and see if I am forgetting something important or if there is a better way.

I did read-up on some method of self-updating (loading & unloading assemblies, etc...) but it just seemed very unsure and I need this to be as robust as possible - if it fails it means someone needs to manually intervene.

Any help or hints would be much appreciated.
Thanks,

I don't believe Launcher.exe needs to be a service, it's just needs to run under an account that has sufficient permissions to stop the main service, replace the files that need replacing, and restart the service.