Cats have filthy mouths. Everyone needs to understand that you have to take cat bites very seriously. If it breaks the skin, go to the doctor and get started on anti-biotics or risk emergency surgery and possible loss of limb. I didn't know how serious it was until my wife was bit, and I feel like most people don't really know either. The most messed up part is navigating the hospital system. They ask a bunch of ridiculous questions and want to kill the cat to check for disease or quarantine with some silly rules for a long time. Basically, if it's your cat that bit you, you have to lie just to get treated.
On another note, I feel like if the OP had accidentally trapped an extra rooster, no one would even blink at suggestions to kill it.
