Hi there. I have trapped three "feral" strays in this way, in the meantime I caught my own cats many times, the neighbours cats frequently and a fox!
Don't worry too much, they settle down quite quickly when they realise they're caught good and proper, and it's easy to release the wrong captee
but when you do get the white boy, throw a towel over the trap before transporting him, this will calm him and help you to present the vet with something other than a spitting hate filled nightmare.
Be sure to put a plastic sheet down in your car, as its a dead cert he will wee in the trap the moment you put it on your car seat.