How to set the InnerException of custom Exception class from its constructor

You set the inner exception by calling the base ctor:

public MyException(string message, Exception innerException)
       : base(message, innerException) {...}

If you need to run some code to get the exception, use a static method:

public MyException(SomeData data) : base(GetMessage(data), GetInner(data)) {...}
static Exception GetInner(SomeData data) {...} // <===== your type creation here!
static string GetMessage(SomeData data) {...}