Complete the eccentric billionaire's rather unusual last will and testament by choosing the appropriate word.

My entire fortune of vintage yo-yos shall go to ___ of my nephews manages to walk the dog for a full minute.

The correct answer is whichever.

We use whichever as a nominal relative pronoun when referring to a restricted, specific choice from a defined group (in this case, "of my nephews"). Whoever is used for open, unlimited groups and does not naturally pair with an "of" phrase in this manner.