The name “Nancy” indeed originally was a nickname for “Anne.” But that does not mean that there is a “St. Nancy” that makes the name “Nancy” appropriate as a confirmation name. The closest established saint’s name I can find is St. Maria Chiara, who was also known as “Clelia Nanette.” Explain to the child that a confirmation name is not chosen solely on the basis of liking a particular name but because the confirmation name actually belongs to a blessed or saint who has that name.
On the other hand, though, it should be said that a parent could choose to name a daughter “Nancy” in honor of St. Anne, who would then be considered the child’s baptismal saint. That is because parents naming children are not required to limit their choices solely to an actual saint’s name but may also choose names that are Christian in origin. But the saint who is honored by the name “Nancy” is St. Anne, not “St. Nancy.”