Well, I am going to offer a completely diffferent opinion.
I think it is all a "connectability" with the cat. On a mental line of thinking. I talk to my cats, they are free to do as they wish. I think the calming influence is based on trust. Eye to eye contact, a calm mind as they are spoken to,
trust.
We take care of several outdoor ferals. They cannot come inside. We have housecats with different personalities who would not agree with the others. So the heirarchy is set up, according to them and how we are able to read them as humans.
Our ability to understand our feline friends depends on us to read them. But I have been sucessful through observation, of getting each and every one into a carrier to the vet. Even the ferals.
Nothing wrong with the Feliway scents, etc. But I think being able to connect on an animal (we are animals) level with them will make the difference. I only have one cat who refuses this...she heard the trap door slam when I caught her to have her spayed...She has never forgiven me. This is the only relationship I have not yet been able to rebuild. But she does accept food and safety.
I learned from her, as we learn from each of our cat brothers. Never again have I used a cat trap on a feral. I talk to them first, and pick them up by my hands after the trust is formed, and take them to be spayed or neutered.
Cats are a unique species and very intelligent. Try to learn to communicate on their level, and loading them into a carrier has been fairly easy for us. Take your time, don't rush the relationship, talk to your cat, and allow a trustful relationship ship to build.
Observe their ways first. Learn the ways of the cat. Eye contact. Calm speech. Trust. And you can pick them up and they will trust you.
I could go on about an incident that happened a few weeks back....but I needed to help a feral who had been lost for 4 days. Calling him back with the voice of the cat, returned him to my house and safety. He heard me cat-call and his name I had given him. He came home. And now he is safe, forever. Would he have walked into a carrier? Yes. He trusts me.