Animate CC is the tool that you'd use to modify Flash content. You'll need the source file (.fla), which will compile to the Shockwave Flash (.swf) file that's actually executed by the web browser. If you just have the .swf and the original designer is long-gone, it's probably easier to just re-build the menu with HTML and JavaScript, especially if that's your core skill-set. There *are* decompilers and things available, but they're not just "one-click and you're good" situations.
If you *do* have the source, Animate CC is basically a WYSIWYG editor, so you can probably figure it out, but if not, like most things, there's a learning curve. You'll need to make a decision about whether it makes more sense for you to hire an expert to knock out the change quickly, or for you to invest a couple hours in getting up to speed.
If you want to get up to speed, there's a great series on lynda.com that will get you going in relatively short order.
If you have actual questions about the tool, this will be the right place to ask.
Hope that helps!