I am assuming the symbol you refer to is more than just a single color. Otherwise there'd be little need to worry about breaking the symbolic link or other Appearance Panel options to alter a one-color symbol.
So.. assuming a multiple color symbol....Set up artboards with the symbol on them... same symbol....
Now using the
Symbol Panel, drag the symbol to the New icon at the bottom of the panel to duplicate it.
Now double click the duplicate symbol and edit that symbol to your heart's content. And click the little "done" arrow when you're happy.
Now select a symbol on one of the artboards.. and in the Control Bar across the top of the screen. Select the Replace menu and choose your edited symbol....
Repeat as desired.
This way you are just editing symbols without breaking any links or altering the original symbol. I'm really not sure if it's any faster than just breaking the original symbol link and editing. However, if retaining symbols is a concern, this is how to do that. Short of using the
Symbol Stainer Tool, there is no direct way to alter the colors within a symbol without breaking the link, or editing the symbol directly.
Screenshots/animations show Illustrator CS6 because I hate the CC subscription model and just prefer working in CS6. However, I do have the latest AI version... if there's a hiccup or something different in CC just let me know and I'll look.