Edit: It's also possible you can use an adapter to plug a mouse into the charging port. It is a USB port. Something like this:
I would say that's also a long shot, but the underlying android OS might possibly recognize the input and provide a means to interact.
+1 to this suggestion. Using a USB OTG Cable will work. I've used one on my Nexus 7 before to plug a wireless mouse into, and it worked fine (brought up the cursor and such). They're pretty cheap as well.