I did not actually understand what problems you are having - if you are asking how to start another application from your app, you should use something like:
- System.Diagnostics.Process.Start("some_path\other_app.exe")
which should be placed in your Timer's event handler, with Timer.Interval set to 60000 ms.
This will start your other app, which should close itself when it's done. This other app will use some memory, but if you need the job done, I guess it is up to you to write the simplest possible program which does what you need.
The other thing that might be concerning you is that your Timer app by itself probably uses ~20Mb of your memory, because it is running under .NET CLR. There is no cure for that :) - the only option to get rid of .NET is to use native C++.
On the other hand, if you're doing this for home use and need to do some simple file handling, why don't you just use Windows' task scheduler and add a repetitive task for some batch or cmd file?