For years, I have campained against plugging a zapper into the wall using a power adapter. I see a risk with this although they are generally safe. The exception is a medically approved power adapter.
Using a medically approved adapter with your current zapper should be as good or possibly better than buying another one, depending on what model you have.
I would certainly recommend getting at least a dual frequency zapper, quad frequency zappers may be even better but I have not tested any of them.