I have a real human skull used for teaching and demonstration in my medical office. It sits on a shelf above my desk. My Torah study books are two shelves down, are they OK there? By having it here am I ritually impure? Can a Kohen enter my office with this present? If I don’t touch it am I OK, and do I have to go into a Mikvah if I do handle it. Interesting question, eh?
Definitely an interesting question. In the Hebrew counterpart of this site Rav Ya'acov Ariel shlita of Ramat Gan answers most of your questions. If the skull belongs to a non-Jew, a kohen may enter your office. By handling it you become ritually impure, but touching it wouldn't be worse than going to a graveyard which requires only washing of the hands upon exiting. All of us are basically ritually impure in our times and therefore there are restrictions entering Har Habayit. This ritual impurity will only be resolved only when we have a "para aduma". Your torah study books are Ok.