Most people wouldn't use the term "Cheeky monkey" as anything but a term of endearment - exactly as it should be received.
I feel like this is a recurring sentiment on this thread: telling people how they should interpret something, and that it's entirely their fault for being offended.
Being inadvertantly offensive or intrusive is one thing.
Continuing to be so, ignoring all context and dismissing anyone's explanations as to why it's irritating to get the same comments/questions over and over, or how a word like 'monkey' has historically been used (and continues to be used: see football chanting, anti-Obama rallies, etc) as an insult towards certain groups... it's your choice.
But there seems to be so much petulance and mock-outrage (throughout the thread not meaning to aim all this at Fluffy) at being asked to consider or modify, even for a second, your own language and behaviour. And all the hyperbole: 'so I should just CENSURE myself', 'so I just shouldn't speak to ANY black people', 'so I can't even call MY OWN CHILDREN a monkey' like Bertrand said, it's just part of the 'political correctness gorn mad' rhetoric, which somehow manages to switch the stakes so that the person saying something offensive is the oppressed party, bravely standing their ground against the Thought Police.
Say what you want! There are a few words which are unequivocably racist. There's a much, much larger grey area of terms and questions that might cause offense, depending on the situation. But if someone explains how X makes them feel, and why, you don't get to tell them: nope, you're wrong; you don't really feel like that, or you're just making it up to be difficult.