Yes, any 9v is fine
Your Zapperplans.com Zapper draws less than 10 milliamps while Zapping and nearly nothing (less than 1 milliamp) when not actually Zapping. This lower power usage (half while in use and a tenth in standby) is a result of the advanced miniature circuitry employed and results in much longer battery life even though the output is the same as the original Geoff Clark design.
We do recommend you disconnect the battery after Zapping since even the small standby current will dissipate your battery after a while.
With care, a typical alkaline battery should last for dozens of Zappings and rechargeable batteries are definitely a good idea. NiMH batteries last longer per charge than NiCad, but they cost more too. NiCad's are pretty inexpensive and should last for over a week of daily Zapping on a charge.
You can also use a 6 cell battery pack with AAA, AA, C or D batteries if you can find one. These kinds of batteries can be lower cost in the long run as they carry comparatively more charge. Here's a good place to start for low cost batteries: