<p>In a class diagram, is there a way of specifying that a class is an internal class of another class ? </p>

<p>Or is it considered as a pure implementation choice ? </p>

For this kind of thing you have separate Diagrams showing the internal structure or processing of a class.
usually, those extra diagrams are activity diagrams to show processing.  Sometimes one per method.  You might also have an internal sequence diagram showing the API interactions.
No reason you can't have an additional class diagram to show internal structure of a class.