Plain white vinegar is the solvent you'd use to neutralize and clean battery corrosion. If it's not too bad, use a brush (an old toothbrush works well) and q-tips to scrub the terminals and battery compartment. You can rinse with distilled water and, if they're rusty, sand the terminals with fine emory cloth. You don't need to clean all the rust necessarily but you do need to expose bright metal to make them conductive.
It won't hurt anything to get vinegar and water inside electronics (particularly distilled), just let it dry before you power it up. Most things made now use water-soluable flux when they solder so finished assemblies are put through what looks like a dishwasher to clean them.
"Silent enim leges inter arma." -- Cicero