Instantising a class via reflection using a constructor with a functional interface

If i have a class, that has a private interface inside, which has the @FunctionalInterface annotation, and a private constructor which takes an instance of a class that implements this interface, how can I construct this object using reflection with my custom implementations of the said interface? For instance:

public class mcve {
  private mcve(mcve.wrapper<String> wrp1, mcve.wrapper<String> wrp2) {
    // ...
  }
  private mcve(mcve.wrapper<String> wrp1) {
    // ..
  }
  public static final mcve INSTANCE_1 = new mcve(ClassExtendsString::new, ClassExtendsString::new);
  public static final mcve INSTANCE_2 = new mcve(ClassExtendsString2::new, ClassExtendsString2::new);
  @FunctionalInterface
  interface wrapper<O> {
    O wrap(O object) throws Exception;
  }
}

and some code trying to accomplish what I want:

 Constructor<mcve> constructor;
 constructor = mcve.class.getDeclaredConstructor(??.class);
 constructor.setAccessible(true);
 mcve testInstance = constructor.newInstance(?? MyCustomClassExtendingString::new);

How do I proceed? The compiler complains about Object not being a functional interface. I'm not sure what to pass to getDeclaredConstructor and newInstance.