I don't get the angst over re-gifting.
If it is something your niece would like AND it wasn't a gift from someone who will be there when she opens it OF COURSE it is a nice present.
Except in this situation the present is used. I would just offer it to her with a quick explanation and not to to pass it off as a gift, which implies thought and expense.
I'd give it to her.
Last year someone gave each of my children a box of chocolates (but they were adult chocolates that looked quite expensive and imported). The person that gave them was a professional and also a health nut.
I suspect the chocolates were all Christmas gifts to that person as they werent really something you'd choose for a child if you were going to give them chocolates; but you know what, its the thought that count and my children loved them so who cares and I think its great that they didnt go to waste and went to people who appreciated them.
That's a very charitable way of looking at it. Because I'm mean I'd also think "so these chocolates are too unhealthy for the giver to consume, but he thinks it's ok for my kids to eat them. Because he doesn't care about my kids' health...". I am my mother's daughter on that one...