Regular alkaline batteries work just fine. The battery chemicals cannot normally leak out unless the battery gets damaged in some way. The reason for "mercury free" batteries is to help eliminate extremely minor contributions to environmental contamination in landfills. So, you don't need to worry about any of the chemicals getting into your body.
If you want your batteries to last longer you will need to get or make your own more efficient Zapper like the one at Zapperplans.com for $10. Otherwise you will have to live with 5 Zappings per battery.