I'd advise you to use "Quique" instead of this, because even though it's pronounced differently (KEE-keh), the English speaking world has a word of the same spelling that is a slur towards Jewish people (pronounced as "kyke"). As such, this could very easily be confused for that. So please, if your kid is named "Enrique", have the Quique spelling of the nickname used instead of this particular spelling.
Due to the fact that this is a slur that mocks people of Jewish descent, I would not suggest using this name to name your kids or to use it as a nickname for Enrique or other names.