Yes, cats are smart. They rarely fall easily for the cage trap twice. Do you have a regular small dog cage? That is what I use, my cats are too big for a small cat carrier, so I have one that is for a small dog, lol. What I have done before is leave it out, open, leave treats in it on occasion, and just ignore it. Then the cat starts to think it's just there, and you aren't going to do anything with it. Then they are a little more likely to go in there after a treat, after they have been in there several times when you weren't looking. But hopefully it will heal and you won't have to take him in. I never did with my cat Taffy, who ended up with the tail bite. I did however have to bring the other cat, the instigator, Beep, to the vet, because in one of their "scuffles" she ended up with a scratched eye. It was swollen shut. My cat Beep is 11, and she has to live a separate life from my other cats, she is the most vicious little demon. She is a tiny 8 1/2 pound little thing with no front claws, whereas all of my other cats have claws, and she kicks the patooties out of any other cat that crosses her path. So we have a schedule, so everyone gets time out evenly, and every one has a comfy window and cat tree in their own rooms when it's their time up. It sucks, but it is a way of life now for us.
How is the tail looking today? Any better? Hoping that it will heal on it's own.