Connecting is easy. Open the battery compartment of your zapper, remove the battery, and connect the matching connector from your adapter. *But do not do this yet.*
The hard part is making SURE that the adapter's output voltage and polarity are correct. The best way to do this is with a voltmeter. Almost anything will do, analog, digital, large or small. I don't know what you have, or have access to, or how much hubby knows about this, so here we go.
Voltmeter, Multimeter, or VOM. Usually there is a function/range selector and 2 or 3 inputs. Also, two leads or test probes, one red and one black. The red one goes to the + or V input, and the black one goes to the - or Return or Ground input. If it isn't auto-ranging, set the range to something greater than 9 volts DC. Usually there is a 12V or 20V range on analog meters, and 19.99V on digital ones.
Next, remove the battery from your zapper and use it to test the meter. With the + (red) probe to the + (small) terminal, and the - (black) probe on the larger terminal, the meter should read somewhere between +8.5 and +9.5 volts. If so, you can trust the probe polarity for the next steps. If not, let me know what you have and how it is behaving.
Next, adjust your AC adapter to 9V, and plug it in. Do NOT connect it to the zapper yet. Use the meter to measure the output voltage of the matching 9V-style connector. In this case, touch the black probe to the *small* terminal and the red probe to the larger one.
Don't be surprised if it reads higher than 9V. I have two older universal adapters. On the 9V settings, one reads 10V and the other reads 12V. There is a sound electronic reason for this, but the main thing here is that your zapper draws much less power than the adapter can supply, and that has consequences. You might have to dial your adapter down to 7.5V or 6V to get an output close to 9V when nothing is connected.
While measuring the output of the adapter, pay attention to the polarity of the reading. Your adapter has the ability to reverse the polarity of the output, but the photo doesn't show how this is done. Usually, it is either a small switch (marked + and -) or a connector in the output cable which you can unplug, reverse, and plug back in. Getting the polarity correct is very important here. Not all zappers have protection from a reversed power connection, and can be damaged almost instantly.
Get back to me on the measurement and polarity, and we'll wrap this up.