I'm not sure if I entirely understand your question, but allow me to try to answer it anyway:
You're asking if it's possible to load your class in such a way that it knows which of the exceptions it might generate, are being handled in the class that's loading the dll? This seems impossible, simply because of the calling hierarchy. What I would suggest is that you document which exceptions may be thrown in your classes, using this mechanism:
/// <exception cref="ArgumentOutOfRangeException">Thrown if argument is greater than the size of the array.</exception>
That way your calling classes can be better prepared to handle the exceptions, and know more or less which possible exceptions aren't being handled.
Another approach is to encapsulate your code in try-catch blocks, and use the fact the more specific exceptions are handled first. You can then handle the scenarios you can resolve programmatically, and then catch the generic Exception last to ensure your program remains stable even if underlying classes fail catastrophically.
Unfortunately I don't see how you're going to tell your called dll, which of the exceptions it might throw are being handled.