Refactoring while you're already in the code is sometimes easiest, especially if your manager does not support the initiative, but if you only change a small part it will break consistency with surrounding parts. In these cases it's better to be selective and, as you suggested, do things that are low-impact. It may also be helpful to refactor long select/switch statements into functions and delay on refactoring the inner code until sometime later.
At a previous job, I was the manager, so I refactored whenever I wanted. At my current job, I'm an analyst so most of the code is not directly my responsibility. When I do write code, I avoid impacting anything that I'm not writing. I have one project which is entirely under my own control and I refactor any time I learn a better way to do something.