I was thinking it's a task you might give a work-experience kid or put out onto RentaCoder
This depends mainly on the codebase's size.
I've seen three trainees given the task to go through a 2MLoC codebase (several thousand source files) in order to insert one new line into the standard disclaimer at the top of all the source files (with the line's content depending on the file's name and path). It took them several days. One of the three used most of that time to write a script that would do it and later only fixed the files where the script had failed to insert the line correctly, the other two just ploughed through the files. (The one who wrote the script later got a job at that company.)
The job of manually adapting all those files in that codebase to certain coding standards would probably have to be measured in man-years.
OTOH, if it's just a few dozen files, it's certainly doable.
Your codebase is very likely somewhere in between, so your best bet might be to set a "work-experience kid" to find out whether there's a tool that can do this to your satisfaction and, if so, make it work.
Should files be left alone until some 'real' change is needed, and then updated?
I'd strongly advice against this. If you do this, you will have "real" changes intermingled with whatever reformatting took place, making it nigh impossible to see the "real" changes in the diff.