Oof this is such a tricky situation. Most vets will need the cat in some sort of carrier (must NOT be in a trap) which itself is really really hard. Then there’s also the issue of their staff does not want to risk whatever could happen to try to calm the cat- feral cats are feral- even the friendly ones. Honestly, feral cats are resilient. We’ve had one that was hit by a car and thought was a goner but she’s stronger than ever LOL. Best of luck…. Most vets won’t even treat a feral… worth a few calls around though