My Norwegian Forest Cats go for walks on harnesses (mainly just to forests but occasionally to the beach or with the dogs next door etc) however I
do have problems with them wanting to be outside all the time. Miss Boopy had never been outside until she got here and within a few days of realising that she can go outside in the run here she wants to be outside all the time and sits and shouts and shouts at you until you let her out and Bilbo pretty much lives outside all the time out of his own choice.
You don't get too many strange looks but once he is a bit older and starts to get big you will get comments of 'that cat is enormous' and 'mummy mummy that's a funny looking dog, no dear it's just a giant cat' etc and also people asking why you are taking them for walks if you walk him in a public place. Mae sure he is fully used to his harness and lead and happy with them before you start taking him out on them.
I think I sent you a link for where to buy really good strong leather harnesses from (I can resend you the link if you haven't still got the PM) Bilbo loves his walks so much brings his harness to you if he wants to go on one bless him
P.S: Bilbo would also like to pass on a message to your Maine Coon that if people accuse him fro a distance of being a dog when on a walk then he should give them the "Look how big I am, you really want to mess with me?!" look and to tell the humans that his slave walks where he wants to go
not the other way around like a dog would.