It's really interesting to read the responses. One of the other reasons we want the skip is just in case we ever do move him to a conventional public school we want him at least a little closer to his actual level without having to fight for it.
Where I live what grade you've called the child while homeschooling is entirely irrelevant to how they will be placed in school. They will be placed in the grade where they fit chronologically unless you have test scores and a portfolio to support a grade skip. Having called the child a particular grade bears no weight in that decision.
It has worked well for our homescholing family to simply deemphasize grade distinctions entirely. We didn't want our child to be invested in those distinctions because he didn't fit them neatly and talking about them only served to emphasize how atypical he is. And, we wanted maximum flexibility to decide what we'd do later (we ended up doing a four year grade skip which feels comfortable with a teenager but would have felt really awkward with a five year old!) I am not uncomfortable saying the child's age because factually that is his age. If people observe wow he seems advanced for his age, I simply confidently agree with the truth of that observation. To me that sends a message to the child that we are comfortable with his development.
For what it is worth, if you are confident and comfortable and don't feel a need to explain, people (including your child) tend to pick up on that. The idea that grades are different in homeschooling is one that people can understand - trust me we've had this conversation about a billion times with random strangers and it has been fine.