Advice on adopting a stray?

Hi everyone.

About a month ago a very skinny and very cute cat appeared on my
doorstep and we started feeding him. I called every shelter and animal
rescue organization and they don't have any reports of him or a lost
cat that is even close. I would love to adopt him, but I am not sure
what I need to do to make that possible.

I have 2 indoor cats already (and hadn't intended to get another one,
but I think he adopted me) and I am not entirely sure what the risks
are. I know I have to take him to the vet before he can come inside,
but will that make it safe to introduce them over time?

My other question is: Does anyone have a good idea for trapping him
without scaring him to death? I looked at the hav-a-heart traps, but I
am afraid of getting all the neighborhood cats but him. If you have
any ideas, please let me know. He's such a pretty cat and he seems
really sweet the less he is afraid of me.

Thanks so much,

Anna