I went to the website and read up on your unit. I don't agree with everything they say about AC adapters - a gigantic surprise around here.
Yes, low cost AC adapters have some ripple ("hum") on the output. So what? This will add a very small 50Hz component to the Zapper output, nothing more. Also, it will not mess with the sacred "DC Offset". Here's the good news - because most zappers are such low power devices, the ripple almost certainly will be *less* than it would be for whatever device the AC adapter was intended. In fact, it might be difficult to measure with "normal" test equipment.
Without knowing more about the guts of the zapper you have, this will take a bit of back-and-forth. Also, there is risk. Connecting the AC adapter incorrectly, even for an instant, could damage your unit beyond repair.
The hard part on your end is finding an AC adapter with a connector on it which mates to the battery connector in the zapper. There is a way around this, but it would be easier if you can find the right kind of adapter. If you can:
1. Make sure it is unplugged before you connect it to the zapper.
2. Be careful how you hook it up. On a 9V battery there are two snap connectors. The small one (usually a complete circle) is positive, and the large one (usually broken into 4 segments) is negative. On your AC adapter, the opposite is true.
If you can't find an AC adapter with the correct connector, then we go to Plan B.
Let me know:
1. What kind of AC adapter do you have, or you can get.
2. If you don't have one with the correct mateing connector for the 9V battery, then there are two things we can do with whatever you have. Describe what you have. It should have a label with the input and output characteristics listed.