We don't know

The richest source of detail concerning Han Tzu is Orson Scott Card's short story "Cheater", which first appeared in his InterGalactic Medicine Show e-zine. The story expores Han Tzu's back story and early life. (This is probably the "spin-off" you are referring to.)

I've read the whole story and it doesn't give his age (or the age at which he is drafted into Battle School), only mentioning that he was older than 5. Even if it gave an exact age, it would be very difficult to extrapolate a "current" age, as there do not seem to be references to his age in any other of Card's works or in the film.

So it seems we just don't know.