Adding another answer to the bunch (no pun intended)...
You do need to call the doAnswer method if you can't\don't want to use spy's. However, you don't necessarily need to roll your own Answer. There are several default implementations. Notably, CallsRealMethods.
In practice, it looks something like this:
doAnswer(new CallsRealMethods()).when(mock)
.voidMethod(any(SomeParamClass.class));
Or:
doAnswer(Answers.CALLS_REAL_METHODS.get()).when(mock)
.voidMethod(any(SomeParamClass.class));