I really just want to make one tiny change to one of my high ranking articles, but I don't want to hurt its rankings at all. Will this mess it up?
It may do. I've made changes to articles before and some have stayed where they were in the search engines while others dropped.
IMO, although it may not cause anything to happen, I wouldn't touch it.....unless you have to make a major change such as an correction to the url in your resource box, etc.