There is a product on the market that traps and kills rodents by
electrocution.  The mice or rats are concealed from view because they are
contained within a box once they are killed.  By baiting them with
something more tempting than your grain (peanut butter maybe?), you may
succeed in keeping them away from the exhibit.

I took the liberty of looking it up for you.  The company is called
Agrizap, and the product is called the "Rat Zapper."  Thier web page is:

        http://www.agrizap.com/

I have no idea what these devices cost, but they can't be too expensive.  I
hope this helps.

Regards,
------
Christian C. Burke
Project Manager
Inter-Con Security Systems, Inc.
Los Angeles County Museum of Art <http://www.lacma.org>