That looks like your puppy. I would guess that those thicker ones (the ones to the left of the pic) go to the rectifier/regulator then to the battery (larger due to increased current going through them) but this may be a camera trick. My money is on the other two going to the ECU for a signal. Here's what you can do:
1. Follow the wires, at least one of which will probably end up at the ECU
2. Find where the other goes (probably to the ECU also)
3. Run the quad if you can and join the two wires with another wire or bit of metal (leave the original wires plugged in, just 'short them' with the new wire)
4. If the quad stops, you've either just sucessfully created your first kill switch, or bust something

- My money's on the kill switch though.
5. With the piece of spare wire or metal still crossing the two, try to start the quad. Everything should work, the engine should turn over, the fuel pump come on etc, but it should NOT spark because you're interrupting the crank signal to the ECU.
6. Take away your spare wire and try to start again.
7. BOB BOB BOB BOB BOB
If you were to cut these wires and attach a kill switch across them, common sence should prevail - make the joint under the nose and out of waters and harms way. DO NOT cut corners, make sure you shrink wrap or tape up (with good quality electronic tape) your new connections, don't just leave it loose and exposed. If your wheel falls off, it's nothing that a rock and zip-tie can't fix to get you home. If your kill switch stops working because of negligence, you better get looking for tree branches that turn into copper, or a good rope and a friendly quadder.
Regards,
_Chipwiz_Ben_