Good point
Underneath all that fur, it would be hard for Cody to blush or show he's blushing.
Artistic reasons aside, I recall Vince wrote a little bit in a future issue where Cody complains to Doug that having a thick coat of fur was annoying due to static electricity and having difficulty in his muscles showing underneath. So arguably, if the fur shows muscle definition, then perhaps it's thin enough to show when Cody's face is turning red.
Plus, let's not forget that some comic characters like Starfire or Beast Boy who both have different-colored skins have shown to show blushing despite it technically would be difficult to do so with their complexions.