When we adopted our "little boy" he was an indoor-outdoor cat in his previous home, prior to that he was a stray younster. We live close to a busy road so he was made into an indoor kitty. NOT by his choice. I was afraid of fleas, another animals starting to come and spray around if he was out, or he would take off. After 5 years of being indoors, I couldn't torture him like that anymore. I love being out, and even though he was in the windows daily, I still felt like that he was missing something. I used to take him for rides in his cat carrier which he would beg for, but this year he seemed to have issues with riding. He would vomit and poop within like 2 minutes of riding. So, he accepted a harness after many attempts. Daily we go out for the morning and night trips around our yard. Granted, I'm sure he hates the harness but it's the only satisfying way I will let him out. Now that it's getting cooler out, he makes a quick trip around the yard, and heads right for the door to come back in.
So where this story was going,was have you considered putting him on a harness (not a collar with leash but a harness with leash) and letting him out? It's more controlled. It took me a little bit to find the right harness size. I ended up with a adjustable medium sized dog harness but it's thin and not bulky (my cat has a wide load attached to him). I tried several and this was the only one that he didn't immediately fight.
Im very glad you got to keep him and take the effort to welcome him into your home...I think strays/abandoned cats realize how lucky they are when they find a good home...