Which pet clinic in Houston handles feral, stray cats?

I am hoping to trap this spicy stray cat in my parents' neighborhood because he's injured and needs to receive some vaccinations, Felv/Fiv testings, and checkups. I called multiple shelters but had no luck. I even brought him to a clinic but the vets didn't want to take the risk of being bitten by an unvaccinated stray cat. I really want to help but don't know who to call at this point. If you know an affordable pet clinic that handles spicy, aggressive stray cats, please let me know.